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!:ST  EXAMPLES 

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MY   HISTORY   LESSONS 

And  Th« 

BOOKS     I    HAVE     READ 


Outjine  Note-books  for  Both 


FLExiBUt  BOAkDs — ^25  Cents  each — blank  book  styl« 

These  two  new  nottbooh  are  a  new  device  that  make  pos- 
sible tlie  keeping  of  a  systematic^  uniform^  concise  and  complete 
record  oK  one's  history  lessons  and  of  the  books  one  reads.  They 
will  be  eminently  serviceable  for  recording  the  data  of  history  les- 
soris,  cr  for  recalling  impressions  of  books  read  j  and  will  be  pecu- 
liarly piacticable  for  teachers — to  place  iii  the  hands  of  students  for 
recording  and  preserving  unpretentious  analyses  of  the  studies  in  his- 
tory, or  of  books  read  in  class  and  in  general  reading.  These  two 
notebooks  embody  an  original  device.  1  he  many  advantages  of  this 
leally  successful  and  popular  device  are  ; 

It  enables  teachers  to  keep  track  of  home  work  and 

to  secure  uniformity  throughout  the  schnol 
It  h  logical.    It  is  pedagogical 
It  is  simple,  concise,  complete 
It  economizes  time  and  labor  ^ 

It  develops  thought,  attention,  discrimination 
It  provides  permanent  data 
It  assists  the  memory 
It  will  develop  the  critical  faculties 
It  encourages  self-activity,  self-direction 
It  encourages  systematic  habits  and  neatneai 
It  is  inexpensive 

The  few  well-arranged  headings  are  so  simple  and  obvious  that 
the  teacher  can  tell  at  a  glance  whether  the  pupils'  history  study  or 
prescribed  book-reading  has  been  done  attentively,  intelligently  and 
thoroughly.    *  Tis  a  teachers'  ^oon,  simply  as  a  teacHers*  r»«-  ■-•/'  *  / 


HINDS,  NOBLE  &  ELDREDGE,  Publishers  of 

How  To  Study  Literature,  75  cents 

Smyth's    American    Literature,     90    cents 

Trimble's  Handbook  Eng.  and  Amer.  Literature,  $1,  3c 

31-33-35  West  J5th  Street  New  York  Qty 


From 
The     Rostrum     (Chicago) 


SEELEY'S    A    NEW    SCHOOL    MANAGEMENT 


This  is  a  readable  book.  It  is  sure  of  a  latere 
sale.  Normal  schools  must  make  it  a  text  1  ook. 
Teachers  will  prize  it  as  a  vade  mecum  while  teaching. 
Teachers'  meetings  will  take  it  up  for  discussion,  and 
we  p-edict  for  it  an  unusual  popularity.  It  is  the 
latest  and  best  book  on  a  live  stibjed  and  is  a  credit  alike 
to  tlie  author  and  the  pubHshers. 

What  Page's  "Theory  and  Practice  of  Teaching" 
was  to  young  teachers  years  ago,  this  new  work  by 
Dr.  Seeley  is  to  young  teachers  of  the  present  age. 
It  is  in  the  highest  degree  a  practical,  helpful  work, 
especially  for  teachers  in  their  first  gear's  work. 
And  for  this  very  reason  it  is  practical  and  helpful 
for  older  teachers  also.  Educational  principles  are 
the  same  everywhere;  they  are  not  graded.  The 
perf.  ct  school  is  a  structure.  Its  higher  depart- 
ments are  built  upon  the  lower,  and  the  pedagogy 
applicable  to  them  all  rests  upon  that  of  the  ele- 
mentary school.  Hence  a  sound  body  of  principles 
illustrated  and  explained  as  clearly  and  fully  as  in 
this  new  book  by  Dr.  Seeley  cannot  lose  its  value  to 
a  teacher,  even  though  he  may  have  passed  on  from 
the  rank  of  a  beginner  to   that  of  a   veteran. 


HINDS,   NOBLE  &  ELDREDGE,  Publishers  of 

School  Management  (Seeley,)  $1.25 

Foundations    of    Education     (Seeley),     $1.00 

Page's  Theory  and  Practice  (with  Quest,  and  Ans.),  $i,oo 

Gordy's      New      Psychology     (for      teachers),      $1.25 

Gordy's     A     Broader     Elementary      Education,     $1.25 

Best    Methods  in    Country  Schools,  $1.25 

Character:     A     Moral    Textbook.     $1,50 

Moore's  Science  of  Study,  $i.oo 

Parliamentary  Usage,  50c. 

3J-33-35  West  J5th  Street,  New  York  City 


Page's 
Theory  and  Practice  of  Teaching 


The  popularity  of  Page's  book  is  perennial.  It  is, 
so  to  speak,  a  staple  with  educators — as  flour  is,  or 
sugar  is,  with  a  grocer.  For  more  than  a  generation 
it  has  been  a  standard  in  normal  schools,  training 
schools,  and  reading  circles.  Superintendents  who 
themselves  studied  it  twenty  years  ago  when  they  were 
just  beginning  to  teach,  now  prescribe  it  at  regular 
intervals  for  the  professional  study  of  young  teachers 
whom  they  are  now  training! 

More  copies  of  Page's  theory  and  practice 
have  been  sold  than  of  any  other  work  on  teach- 
ing. In  States  which  have  a  State  reading 
circle  it  is  always  one  of  the  first  works  officially 
adopted,  and  then  gets  re-adopted  every-so-many 
years.     Its  chapters  cover  : 

The  Spirit  of  the  Teacher 

Responsibility  of  the  Teacher 

Habits  of  the  Teacher 

Literary  Qualifications  of  the  Teacher 

Right  Views  of  Education 

Right  Modes  of  Teaching 

Conducting  Recitations 

Exciting  an  Interest  in  Study 

School  Government 

School  Amusements 

Teachers  Relations  to  Parents  of  Pupils 

Teacher's  Care  of  His  Health 

Teacher's  Relation  to  His  Profession 

Miscellaneous  Suggestions 

The  Rewards  of  the  Teacher 

To  impart  to  the  book  still  greater  value  for 
teachers  who  have  to  take  grade  examinations 
we  have  added  numerous  questions  and  answers 

ON    THEORY   AND    PRACTICE   OF   TEACHING. 

A  teacher  is  sure  to  be  well-equipped  who  possess- 
es Page's  book,  if  in  addition  he  (or  she)  also  possesses 
Seeley's  A  new  school  management,  which  many 
teachers  tell  us  is  the  only  rival  that,  possibly,  excels 
Page's  theory  and  practice. 

HINDS,  NOBLE  &  ELDREDGE,  Publishers  of 

Page's  Theory  and  Practice  (with  Quest,  and  Ans.),  $i.oo 

Seeley's    A     New     School    Management,    $1.25 

Gordy's  New  Psychology  (for  teachers),  $1.25 

3J-33-35  West  J5th  Street        New  York  City 


IN    THB    SaMK    SKRIKS 


lOOI  QUESTIONS  AND  ANSWERS  ON 

U.  S.  HISTORY. 
(Including  the  Federal  Constitution  and  Amendments.) 

lOOI   QUESTIONS  AND  ANSWERS  ON 

GEOGRAPHY. 

(Embracing  Descriptive,  Physical  and  Mathematical  Geography.) 

XOOI   QUESTIONS  AND  ANSWERS  ON 

GRAMMAR. 
(With  copious  Illustrations,  Parsing  and  Analysis.) 

lOOI   QUESTIONS  AND  ANSWERS  ON 

ARITHMETIC. 
(Including  nearly  300  Test  Examples,  with  Solutions.) 

lOOI   QUESTIONS  AND  ANSWERS  ON 

THE   THEORY  AND  PRACTICE  OF  TEACHING 

ICX)I   QUESTIONS  AND   ANSWERS  ON 

FHYSIOI.OGY   AND   HYGIENE. 
(Containing  a  Chapter  on  the  Physiological  effects  of  Alcohol  ani 

Narcotics.) 


XOOI   QUESTIONS  AND  ANSWERS  ON 

ORTHOGRAPHY  AND  READING. 

lOOI   QUESTIONS  AND  ANSWERS  ON 

GENERAIv  HISTORY. 

1001   QUESTIONS  AND  ANSWERS  ON 
BOTANY. 

lOOI   QUESTIONS  AND  ANSWERS  ON 

TEST  EXAMPI.es  IN  ARITHMETIC 

lOOI    QUESTIONS  AND   ANSWERS  ON 

PHYSICS  OR  NATURAL  PHILOSOPH  n' 


EXTRA  ClyOTH,  Prick  50c.  Each.     Postage  Prepaid^ 

HINDS.  NOBLE  &  ELDREDGE,  Publishers 
»*  :'3  35  West  15th  Stret.;.  New  York  Cit> 


• lOOl •  ^ 

THST   EXAMPLKS    i 


IN 


ARITHMETIC 


WlTk  AiNSvvcRS. 


REVISED  EDITION. 


HINDS,   NOBLE  &  ELDREDGE, 
31-33-35  West  15th  Street,  New  York  City. 


^     GIFT  . 

Copyright.  1896, 
THE  BURROWS  BROTHERS  CO. 


CONTENTS.  'Z-fi-u,^, 

h^^ 

Example.  Solution. 

PAGE.  PAGE. 

Fractions, 5  84 

Percentage, 14  92 

Interest 23  loi 

Stocks  and  Bonds, 27  106 

Discount, 35  113 

Exchange, 38  117 

Insurance, 42  121 

Taxes, 45  124 

Duties  or  Customs, :   .   .   .   .  46  125 

Proportion, 48  127 

Partnership, 50  129 

Equation  of  Payments, 52  132 

Alligation, 54  135 

Arithmetical  Progression, 56  137 

Geometrical  Progression, 57  138 

Time, 58  139 

Application  of  Square  Root, 59  140 

Application  of  Cube  Root, 60  141 

Measurements, 61  142 

Miscellaneous, 65  146 


M669ia6 


HOW  TO   BECOME 

QUICK  AT  FIGURES- 


OLOTH,  200  PAaES-PEIOE  $L00. 


It  would  seem  hardly  necessary  to  enter  upon  a  description 
Cn  detail  of  this  book.  Every  one  knows  what  it  is  to  be  shw 
at  figures  !  Who  is  there  to  whom  quickness  at  figuring  would 
not  come  as  a  godsend  !  The  title  of  this  book  means  just  that, 
and  there  are  thousands  of  testimonials  from  grateful  pur- 
chasers who  thank  the  publishers  for  enabling  them  to  become 
possessed  of  that  which  they  had  not — quickness  at  figures. 

Short  cuts  to  everything  !  Not  puzzles !  But  easy  methods, 
plain  and  learnable  by  every  one  !  Replete  with  quick  and 
simple  processes  for  all  operations.  Are  you  a  teacher  of  Arith- 
metic and  have  you  examination  papers  to  correct  ?  Are  you  a 
teacher  of  anything — not  Arithmetic,  and  have  you  percent- 
ages to  figure  ?  Are  you  a  pupil  and  have  you  time  to  be 
saved  ?  Are  you  a  clerk  ?  Are  you  an  employer  ?  Do  you 
ever  buy  anything  ?  Do  you  ever  sell  anything  ?  Do  you  ever 
measure  anything  ?  Do  you  travel  ?  Do  you  want  tc  be 
more  clever  than  you  are  ? 

If  you  wish  to  please  a  friend,  present  a  copy  of  "  How  to 
Become  Quick  at  Figures."  If  you  want  to  please  your  em- 
ploy'er,  present  yourself  with  a  copy.  If  you  want  to  surprise 
your  teacher,  get  a  copy  and  use  it.  If  you  want  to  delight 
your  pupils,  instruct  them  in  its  methods.  If  your  clerks  are 
slow,  have  them  study  it.     li you  are  not  quick  at  figures — ! 

If  you  want  to  put  yourself  in  a  position  to  demand  higher 
wages,  what  may  you  do?  If  you  wish  to  spend  your  leisure 
time  profitably, — ^your  vacation,  say— send  for  our  terms  to 
agents,  and  go  to  work,  and  discover  for  yourself  how  readily 
this  book  sells. 


Price    $1.00. 


FRACTIONS. 


1.  A  "boy  engages  to  cut  each  stick  of  a  cord  of  wood  in  two 

pieces  at  50  cts.  per  cord.  What  should  he  receive  per 
cord  for  cutting  each  stick  in  three  pieces  ?    Ans.  :  $1. 

2.  Two  consecutive  numbers  are  such  that  \  of  the  less  ex- 

ceeds ^  of  the  greater  by  one  ;  find  the  numbers.  Ans.  : 
80  and  95. 

3.  Two  numbers  differ  by  28,  and  one  is  f  of  the  other  ;  find 

them.     Ans.  :  252  and  224. 

4.  Find  a  number  whose  |  part  is  less;  than  its  J  by  3.     Ans.: 

60. 

5.  What  number  is  that   whose  ^  and   |  are    equal  to  15? 

Ans.:  54. 

6.  I  of  A's  money  is  equal  to  B's,  and  |  of  B's  is  equal  to  C's; 

all  together  have  $770  ;  what  has  each  ?  ANS. :  A,  $450 ; 
B,  $180 ;  C,  $140. 

7.  The  width  of  a  room  is  f  of  its  length ;  if  the  width  had 

been  3  ft.  more  and  the  length  3  ft.  less  the  room  would 
have  been  square.  What  are  the  dimensions  ?  Ans.  : 
12  and  18. 

"8;  A,  B  and  C  together  have  6450  sheep.  C  has  twice  as  many 
as  B,  and  if  120  be  taken  from  A  he  will  have  ^  as  many 
as  B.  How  many  has  each?  Ans.:  A,  753;  B,  1899;  C, 
3798. 

9.  The  difference  between  J  and  J  of  a  number  is  6  less  than 
I  of  the  number.    What  is  the  number  ?    Ans.  :  180. 

10.  f  of  a  number  of  persons  received  15  cts.  each  and  ^  re- 

ceived 9  cts.  each.  They  all  received  $4.68,  How  many 
persons  were  there  ?    Ans.  :  36. 

11.  If  $45  is  f  of  my  money,  T»hat  part  of  it  will  that  sum 


plus  $4^  be  ?    Ans. 


FRACTIONS. 


12.  A  and  B  can  do  a  piece  of  work  in   12  days.     Assuming 

that  A  can  do  |  as  much  as  B,  how  long  will  it  take  each 
to  do  it  ?    Ans.  :  A,  28 ;  B,  21  da. 

13.  A  and  B  together  had  $5,700.     |  of  A's  money  was  equal 

to  f  of  B's.  How  much  had  each  ?  Ans.  :  B,  $3,000 ;  A, 
$2,700. 

14.  A,  B  and  C  have  $540.     \  of  A's  share  is  equal  to  \  of  B's 

and  f  of  B's  share  is  equal  to  f  of  C's.  How  many  dol- 
lars has  each  1    Ans.  :  A,  $240 ;  B,  $160,  and  C,  $140. 

15.  Two  men   found  a  purse,   the   contents  of  which  they 

divided  equally.  A  takes  for  his  share  $1,000,  and  y\  of 
remainder.  How  much  did  the  purse  contain  ?  Ans.  : 
$2,444f. 

16.  The  sum  of  two  numbers  is  490,  and  one  bears  the  same 

relation  to  \  as  the  other  does  to  f .  What  are  the  num- 
bers ?    Ans.  :  196  and  294. 

17.  The  sum  of  two  numbers  is  1,357.    Their  difference  is  xt 

of  the  smaller  number.  Find  the  numbers.  Ans.  :  649 
and  708. 

18.  A  sold  B  a  horse  for  \  more  than  it  cost  him.     B  sold  it  to 

C  for  $36,  which  was  \  less  than  it  cost  him.  What  did 
A  pay  for  it  ?    Ans.  :  $40. 

19.  A  can  do  a  piece  of  work  in  5  days  ;  B  can  do  the  same  in 

7  days.  How  long  will  it  take  them  together  to  do  the 
work  ?    Ans.  :  2\\  da. 

20.  A  man  and  his  wife  use  a  bag  of  meal  in  16  days ;  it  will 

last  his  wife  alone  48  days.  How  long  will  it  last  the 
man  ?    Ans.  :  24  da. 

21.  A's  land  is  \  less  in  quantity  than  D's,  but  2V  better  in 

quality;  how  do  their  farms  compare  in  value.  Ans.  : 
A's  i»o  of  D's. 

22.  If  \  of  A's  sheep  equals  f  of  B's,  what  part  of  B's  equals  | 

of  A's?    Ans.:  f. 

23.  A  has  f  more  money  than  B,  and  B  f  more  than  C.     How 

many  times  C's  is  A's  ?    Ans.  :  2|. 

24.  f  of  my  capital  equals  \  of  yours  ;  if  we  put  both  together 

what  part  of  the  whole  will  I  own  ?    Ans.  :  xV 


FRACTIONS. 


25.  After  selling  \  and  \  of  my  horses  I  had  8  more  than  I  had 

sold ;  how  many  had  I  at  first  ?    Ans.  :  80. 

26.  In  12  years  I  shall  be  \  of  my  present  age ;  how  long  since 

was  I  f  of  my  present  age  ?    Ans.  :  ^\  yrs. 

27.  Four  times  f  of  a  number  is  100  less  than  twice  the  num- 

ber ;  what  is  the  number  ?    Ans.  :  90. 

28.  A  man  left  y\-  of  his  money  to  his  wife,  f  of  the  remainder 

to  his  sou  and  the  balance,  $2,100,  to  his  daughters  ; 
what  was  the  estate  ?    Ans.  :  $10,800. 

29.  I  sold  an  article  to  A  for  |  less  than  it  cost  me  ;  A  sold  it 

for  $21,  which  was  f  more  than  it  cost  him.    What  did 
it  cost  me  ?    Ans.  :  $25. 

30.  A  is  J  older  than  B  ;  their  father,  whose  age  is  equal  to 

the  sum  of  theirs,  is  54;  how  old  are  A  and  B?     Ans.  : 
24  and  30. 

31.  A  tree  stands  f  under  water ;  the  water  rose  8  ft,  and  then 

there  was  as  much  under  water  as  had  been  above  water 
before.     Find  height  of  tree.     Ans.  :  i8f  ft. 

32.  A  is  f  as  old  as  B ;  if  he  were  6  yrs.  older  he  would  be  y\ 

as  old  as  B  ;  how  old  is  each  ?    Ans.  :  48  and  60. 

33.  A's  money  is  $9  more  than  |  of  B's  and  $6  less  than  \  of 

B's ;  how  much  has  each  ?    Ans.  :  $99  and  $120. 

34.  f  of  A's  age  is  f  of  B's,  and  A  is  2  yrs.  the  older.     How 

old  is  each  ?    Ans.  :  A,  32  ;  B,  30. 

35.  If  4  boys  do  a  work  in  8  hrs.,  how  long  will  it  take  a  man 

who  works  five  times  as  fast  as  a  boy?    Ans. :  6|  hrs. 

36.  If  10  men  can  do  a  work  in  5  days,  how  much  time  will 

be  saved  by  employing  2  more  ?    Ans.  :  |  da. 

37.  A  left  I  of  his  estate  to  his  wife ;  the  remainder  to  his 

son,  who  received  $900  less  than  his  mother.     What  was 
the  estate  ?     Ans.  :  $4,500. 

38.  B  is  worth  7  times  A  ;  what  part  of  B  is  f  of  A  and  B  both 

worth  ?    Ans.  :  fi- 

39.  Divide  102  into  two  such  parts  that  |  of  the  first  is  equal 

to  f  of  the  second.     Ans.  :  54  and  48. 

40.  What  number  is  that  whose  \  increased  by  8  is  12  less 

than  its  \.    Ans.  :  80. 


FRACTIONS. 


41.  Bight  men  hire  a  coach ;  by  getting  four  more  passengers 

their  expenses  are  reduced  $1  each.     What  do  they  pay 
for  the  coach  ?    Ans.  :  $24. 

42.  I  sell  eggs  at  10  cts.  per  doz.  and  lose  |  ct.  apiece.     How 

much  must  I  sell  them  for  to  gain  \  ct.  apiece  ?    Ans.  : 
25  cts. 

43.  One-tenth  of  a  dollar  is  what  part  of  2|  cts  ?    Ans.  :  \\. 

44.  I  gain  \  ct.  apiece  by  selling  pears  3  for  a  dime ;  how  much 

apiece  will  I  lose  by  selling  them  4  for  a  dime?    Ans.  : 
ict. 

45.  How  much  grain  must  I  take  to  mill  so  that  I  shall  bring 

back  6  bu.  after  paying  toll  at  the  rate  of  4  qt.  to  the 

bu.  ?    Ans.  :  6f  bu. 

46.  After  doing  f  of  a  work  in  30  days,  I  called  an  assistant ; 

we  both  completed  it  in  6  days.     In  what  time  could  the 
assistant  do  it  alone  ?     Ans.  :  2if  da. 

47.  The  sum  of  two  numbers  is  4816.    Their  difference  is  f  of 

the  larger.     Find  the  numbers.     Ans.  :  3612  and  1204. 

48.  A  can  do  a  piece  of  work  in  \  da.,  B  in  ^  and  C  in  a  day  ; 

in  what  time  can  all  do  it  ?    Ans.  :  xV- 

49.  A  can  do  a  work  in  40  days,  B  in  60  ;  after  both  work  3 

days  A  leaves  ;  when  must  he  return  that  the  work  may 
occupy  but  30  days  ?    Ans.  :  At  the  end  of  the  i3th  day. 

50.  A  and  B  can  do  a  work  in  12  days,  A  and  C  in  8  days,  B 

and  C  in  6  days.     How  long  will  it  take  all  together  to 
do  it  ?     Ans.  :  5 J  da. 

51.  A  can  plow  f  of  a  field  in  6  days,  B  f  in  10  days  ;  in  what 

time  can  they  both  plow  it  ?    Ans.  :  5f  da. 

52.  A  and  B  can  cut  a  field  of  corn  in  12  days,  and  A  alone  in 

20  days.     In  what  time  can  B  cut  it  ?    Ans.  :  30  da. 

53.  A,  B  and  C  together  do  a  work  in  12  days  ;  A  alone  can  do 

it  in  24  days ;  B  alone  in  34 ;  in  what  time  can  C  do  it 
alone?     Ans.:  8if  da. 

54.  A  can  mow  3  acres  in  4  days,  B  5  acres  in  6,  and  C  2^  acres 

in  5  days.     In  how  many  days  can  the  three  mow  2\ 
acres?    Ans.:  i^  da. 

55.  Two-thirds  of  a  number  plus  \  of  the  number  plus  34 

equals  twice  the  number.  What  is  the  number  ?  Ans.  :  30 


FRACTIONS. 


56.  The  age  of  B  is  2*  times  that  of  A,  and  the  sum  of  their 

ages  is  76  years ;  what  is  the  age  of  each  ?     Ans.  :  A,  20 ; 
B,  56. 

57.  Divide  88  sheep  among  A,  B  and  C,  giving  to  B  |,  and  to 

C  f  as  much  as  to  A.    Ans.  :  A,  42  ;  B,  28,  and  C,  18. 

58.  Divide  $440  among  three  persons,  A,  B  and  C,  so  that  the 

share  of  A  may  be  f  that  of  B,  and  the  share  of  B  |  that 
of  C.    Ans.  :  A's,  $90 ;  B's,  $150,  and  C's,  $200. 

59.  The  age  of  A  is  twice  that  of  B,  and  B's  twice  C's,  and  the 

sum  of  all  their  ages  is  98  years.     What  is  the  age  of 
each  ?    Ans.  :  A,  56  ;  B,  28  ;  and  C,  14  yrs. 

60.  A  man  having  spent  $3  more  than  |  of  his  money  had  $7 

more  than  \  of  it  left ;   how  much  had  he  at  first  ? 
Ans.:  $75. 

61.  It  is  required  to  divide  91  into  two  such  parts  that  the 

greater,  being  divided  by  their  diflference,  the  quotient 
will  be  7.     Ans.  :  49  and  42. 

62.  Two  persons  can  drink  a  cask  of  water  in  6  days  and  one 

alone  in  10  days  ;  how  many  days  will  it  last  the  other  ? 
Ans.  :  15  da. 

63.  A  could  mow  a  field  in  20  days,  but  if  B  assisted  him  6 

days  he  could  mow  it  in   16  days;  in  how  many  days 
could  B  mow  it  alone  .■*    Ans.  :  30  days. 

64.  What  is  the  value  of  |  of  f  of  f  of  a  pound  at  $y%  for  f  of 

a  pound?    Ans.  :  $|j. 

65.  If  a  certain  number  be  diminished  by  its  ^,  and  f  of  the 

remainder  be  added  to  the  first  number,  the  sum  will 
be  18.24;  find  the  number.     Ans.:  11.52. 

66.  Divide  $125 J  among  A,  B  and  C,  giving  C  $7^^  more  than 

B,  and  $I2|  more  than  A.     Ans.:  A,  $35!;  B,  $41^;  and 

c.  $^^. 

67.  What  number  is  that  which  being  increased  by  its  f  and 

diminished  by  20  is  equal  to  45  ?    Ans.  :  35. 

68.  I  have  in  my  mind  two  numbers;  one  is  3J  times  the 

other  and  their  difference  is  100.    Find  the  numbers, 
Ans  :  40  and  140. 

69.  What  number  is  that  to  which  if  you  add  its  J  ^nd  \  the 

sum  will  exQ.^d  its  ^  by  51  ?    Ans.  :  36,  " 


FRACTIONS. 


70.  A  person  bought  a  number  of  lemons  for  94  cts. ;  having 
lost  7,  he  sold  \  of  the  remainder  at  cost  for  20  cts. 
How  many  had  he  at  first  ?    Ans.  :  47. 

71-  i  +  i  +  i^  of  my  money  is  $18.  How  much  money  have  I? 
Ans.:  $24. 

72.  The  sum  of  two  numbers  is  9f  and  their  difference  is  4|. 

4  times  the  larger  is  how  many  times  the  smaller? 
Ans.:  ii. 

73.  The  owner  of  y\  of  a  mine  sold  ^-^  of  his  share  for  $40,500. 

What  should  a  person  who  owns  f  of  it  get  for  f  of  his 
share?    Ans.:  $70,714!. 

74.  I  of  A's  money  is  to  f  of  B's  as  3  to  4.     They  both  to- 

gether have  $1,520.  How  much  has  each  ?  Ans.  :  A 
$720  and  B  $800. 

75.  A  and  B  together  have  153  sheep  ;  |  of  A's  equals  |  of  B's. 

How  many  has  each?    Ans.  :  A,  81 ;  B,  72. 

76.  A  man  in  walking  18  miles  finds   that  the  distance  he 

walks  in  100  min.  is  f  of  the  remaining  distance.  Find 
his  rate  of  walking.     Ans.  :  One  mile  in  13J  min. 

77.  A  can  do  as  much  in  3  hrs.  as  B  can  do  in  5.     How  long 

will  it  take  A  to  finish  a  piece  of  work  of  which  B  has 
done  I  in  20  hrs.  ?    Ans.  :  4  hrs. 

78.  If  20  men  do  a  work  in  12  days,  how  many  men  can  per- 

form another  work  three  times  as  large  in  \  of  the  time? 
Ans.:  300. 

79.  A  has  \  of  if-  times  $2,660,  which  is  2f  times  as  much 

again  as  B  has.     How  much  has  B  ?    Ans.  :  $420. 

80.  Divide  7,250  sheep  between  A  and  B  so  that  A  shall  have  \  as 

many  asB,  increased  by  1,250.     Ans.  :  A,  4,050;  B,  3,200. 

81.  A  had  f  of  f  of  7^   times  7,862  sheep,  and  sold  \  of  \  of 

them.     How  many  had  he  left  ?    Ans.  :  35,379. 

82.  There  is  a  fish  whose  head  is  12  inches  long,  and  whose 

tail  is  as  long  as  its  head  plus  \  of  its  body,  and  whose 
body  is  as  long  as  its  head  and  tail.  What  is  the  length 
of  the  fish  ?     Ans.  :  96  in. 

83.  A  man  lost  |  of  all  his  money  ;  he  then  found  $24 ;  he  now 

lost  I  of  all  he  had,  and  had  only  $48  left.  How  much 
bad  be  at  first  ?    Ans.  :  $360. 


FRACTIONS.  II 


34.  B  sold  a  cask  of  acid  and  water ;  f  of  the  whole  plus  3 
gallons  is  acid,  and  \  of  the  whole  plus  t\vo  gallons  is 
water.  How  many  gallons  of  each  ?  Ans.  :  Acid,  43 
gal.;  water,  17  gal. 

85.  Find  the  result  of  i  +  fXf^f  —  i-^TV  +  f  X  I  Ans.:  i 

86.  A  bought  a  lot  for  $68,  which  was  f  of  twice  what  he  sold 

it  for,  lacking  $1 ;  how  much  did  he  gain  ?   Ans.  :  $12.50. 

87.  Divide  $542  between  A  and  B  so  that  f  of  A's  part  plus  24 

shall  equal  f  of  B's.    Ans.  :  A's,  $270;  B's,  $272. 

88.  I  of  A's  age  plus  8  yrs.  equals  |  of  B's,  and  the  sum  of 

their  ages  is  148  years.  Find  their  ages.  Ans.  :  A's,  64 ; 
B's,  84. 

89.  What  will  10  yds.  of  cloth  cost  at  $i.o.^|3^  per  yd.?    Ans.; 

$1010. 

90.  If  f  of  A's  number  of  sheep  plus  f  of  B's  equals  180,  and 

\  of  B's  number  is  to  |  of  A's  number  as  f  to  f ,  how 
many  sheep  has  each  ?    Ans.  :  A,  126 ;  B,  128. 

91.  A,  B  and  C  have  $645.     C  has  twice  as  much  as  B,  and:  if 

$12  be  taken  from  A's  he  will  have  \  as  much  as  B. 
How  much  has  each  ?    Ans.  :  A,  $75.30 ;  B,  $189.90 ;  C, 

$379.80. 

92.  A  man  owns  a  pig  and  a  horse ;  \  the  value  of  the  horse 

equals  four  times  the  value  of  the  pig.  Both  together 
are  worth  $170.  Find  the  value  of  each.  Ans.:  Pig, 
$10 ;  horse,  $160. 

93.  If  the  J  of  6  is  3,  what  would  the  \  of  50  be  ?    Ans.  :  15. 

94.  What  will  100  yds.  of  silk  cost  at  $1.00. of ^  per  yd.  ?    Ans.  : 

$600. 

95.  A  is  20  yrs.  of  age;  B's  age  is  equal  to  A's  and  \  of  C's; 

and  C's  is  equal  to  A's  and  B's  together.  Find  the  age 
of  each.    Ans.  :  B,  60  yrs. ;  C,  80  yrs. 

96.  A  is  35  yrs.  old  and  his  son  is  10.     How  soon  will  the  son 

be  \  the  age  of  his  father  ?    Ans.  :  15  yrs. 

97.  A  and  B  can  do  a  work  in  20  hrs.     If  A  does  f  as  much  as 

B,  in  how  many  hours  can  each  do  it  ?  Ans.  :  A,  46! 
hrs. ;  B,  35  hrs. 


FRACTIONS. 


98.  If  to  a  certain  number  you  add  \  of  itself  the  result  will 

be  20  less  than  double  the  number.  Find  the  number. 
Ans.:  26|. 

99.  \  of  A's  sheep  is  equal  to  f  of  B's,  and  the  diflference  is  8. 
'    How  many  has  each  ?    Ans.  :  A,  48 ;  B,  40. 

ICO.  James  Boone  sold  -f^  of  his  sheep  and  then  bought  65. 
He  then  had  |  of  all  he  had  killed  by  dogs,  and  had  left 
10  less  than  he  had  at  first.  How  many  had  he  at  first  ? 
Ans.:  33. 

loi.  A  man  spent  fV  of  ^  ^^is  money  and  then  received  $65, 
and  then  \  of  what  he  first  had  equaled  3^/^  of  all  his 
money.  How  much  had  he  at  first  ?  And  what  did  he 
spend?    Ans.  :  $33  at  first;  spent  $6. 

102.  f  of  5J  furlongs  is  \  of  y^  of  how  many  miles  ?    Ans.  :  lizf . 

103.  A  merchant  gains  a  sum  equal  to  |  of  his  capital ;  the  \ 

of  his  gain  multiplied  by  \  of  his  increased  capital 
equals  4  times  his  gain.  How  much  had  he  at  first .' 
Ans.:  $24. 

104.  A  and  B  have  equal  sums  of  money ;  A  loses  \  of  his 

money  and  B  gains  $100  \  B  then  has  three  times  as 
much  as  A.     How  much  had  each  at  first  ?    Ans.  :  $100. 

105.  A  hare  has  100  yds.  the  start  of  a  hound  ;  the  hare  runs 

'j\  yds.  in  f  of  the  time  that  the  hound  takes  to  run  12. 
How  many  yds.  will  the  hound  run  to  catch  the  hare  ? 
Ans.:  600. 

xo6.  A  owns  ^0  of  a  mine  and  B  j\.  A  bought  from  B  enough 
to  make  his  share  equal  to  what  B  had  left,  paying 
therefor  $3,500.  What  was  the  value  of  the  mine .? 
Ans.:  $60,000. 

107.  Ten  years  ago  the  sum  of  the  ages  of  two  sons  was  \  of 

their  father's  age ;  one  is  two  years  older  than  the 
other  and  the  present  sum  of  their  ages  is  14  less  than 
their  father's  age.  How  old  are  they?  Ans.  :  17  and  15 
yrs. 

108.  A  man  earns  twice  as  much  as  he  had  to  begin  with,  and 

then  spends  $16;  he  loses  ^  of  what  remained,  and  af- 
terwards earns  as  much  as  he  had  at  first ;  he  then  had 
$80.     What  had  he  at  first?     Ans.  :  $52. 


PR  ACTIONS.  13 


109.  $40  is  divided  among  a  number  of  men  ;  if  the  number 

had  been  increased  by-^,  each  would  have  received  20 
cts.  less.     Find  the  number  of  persons.     Ans.  :  40. 

110.  I  spent  $15  more  than  |  of  my  money,  and  then  had  $13 

less  than  f  of  it  left.  How  much  had  I  at  first  ?  Ans.  : 
$80. 

111.  A  boy  gives  f  of  his  apples  to  A,  J  to  B  and  the  rest  to 

C.  C  gives  10  to  B,  and  A  then  has  6  more  than  B. 
How  many  had  each  at  first  ?    Ans.  :  A,  96 ;  B,  80 ;  C,  64. 

112.  Four  times  B's  age  exceeds  A's  age  by  20  yrs.,  and  J  of 

A's  age  is  less  than  B's  age  by  2  yrs.  Find  their  ages. 
Ans.  :  a,  36  yrs. ;  B,  14  yrs. 

113.  y^y  of  A's  age  is  greater  by  two  years  than  \  of  B's,  and 

twice  B's  age  is  equal  to  what  A's  age  was  13  years  ago. 
Find  their  ages.     Ans.  :  A,  55 ;  and  B,  21  yrs. 

114.  J  of  the  sum  of  two  numbers  is  14,  and  \  of  their  differ- 

ence is  4.    What  are  the  numbers?    Ans.  :  25  and  17. 

115.  \  of  the  difference  between  two  numbers  is  4,  and  i\ 

times  their  sum  is  75.  Find  the  numbers.  Ans.:  7 
and  43. 

116.  \  of  the  sum  of  two  numbers  is  16,  and  4  times  their  sum 

and  difference  is  480.  Find  the  numbers.  Ans.:  60 
and  20. 

117.  Bought  4  yds.  of  silk  for  $.00,-^-^^^  per  yd.  and  sold  it  at 

$i.oo2__  per  yd.     Find  my  gain  on  the  whole.    Ans.  :  $4. 

118.  A  man  walks  to  town  at  the  rate  of  4J  miles  an  hour  and 

walks  back  at  the  rate  of  3  miles  an  hour.  He  was 
gone  7J  hours.  How  far  was  it  to  town  ?  Ans.  :  13J 
miles. 

119.  \  of  the  difference  between  two  numbers  is  equal  to  \  of 

their  sum.  The  smaller  number  is  287.  Find  the 
larger.     Ans.:  451. 

120.  B  buys  goods  at  a  discount  of  |  and  \  off  and  sells  them 

at  a  discount  of  y^  and  ^^  off-  What  does  he  gain  on 
the  dollar  ?     Ans.  :  $|. 

121.  f  of  a  quantity  of  milk  and  water  is  milk.     When  I  add 

10  gal.  of  water  the  milk  is  217  of  the  whole.  What  was 
the  mixture  at  first  ?    Ans.  :  70  gal. 


14  PERCENTAGE. 


122.  Divide  12J  into  two  parts  so  that  one  shall  be  \2\  times 

the  other.     Ans.  :  | f  and  iif^. 

123.  I  bought  a  watch  and  chain  for  $48.     \  the  cost  of  the 

watch  plus  the  difference  between  the  watch  and  chain 
equals  the  chain.  Find  the  cost  of  each.  Ans.  :  Chain, 
$18;  watch,  $30. 

124.  I  buy  calico  and  sell  it  at  a  profit  of  \  of  the  cost.     Find 

the  cost  per  yard  if  the  selling  price  of  125  yds.  is 
equal  to  the  profit  on  $30  outlay.     Ans.  :  6  cts. 

125.  If  f  of  $1  buy  5  of  a  sheep  and  f  of  a  sheep  be  worth  j^j 

of  an  ox,  what  will  10  oxen  cost  ?    Ans.  :  $200. 

126.  A  is  20  yrs.  old  ;  the  sum  of  the  ages  of  B  and  C  equals  4 

times  A's  age.  C's  age  is  |^  of  A  and  B  together.  What 
is  the  age  of  each?    Ans.  :  C,  10 ;  B,  70  yrs. 

127.  If  J  of  8  is  3,  what  would  the  half  of  90  be  ?    Ans.  :  67J. 


PERCENTAGE. 


1.  A  man  sold  a  horse  for  $84,  and  by  so  doing  gained  \  of 

what  it  cost  him.  What  %  would  he  have  gained  if  he 
had  sold  it  for  $100  ?     Ans.  :  42f  %. 

2.  A  sold  I  of  a  lot  for  $72  and  gained  $6.     What  would  have 

been  his  rate  of  gain  had  he  sold  the  whole  lot  for 
$100?    Ans.:  I3tV%- 

3.  A  sells  pork  at  $ro  a  bbl.,  \  of  which  equaled  his  gain. 

How  many  %  would  he  have  gained  if  he  had  sold  it  at 
$12  a  barrel  ?    Ans.  :  50%. 

4.  Sold  a  horse   for  $440  and  thereby  gained  10%.     How 

ought  I  to  have  sold  it  to  lose  25^?    Ans.  :  $300. 

5.  A  and  B  invest  equal  sums  in  business.     A  gains  a  sum 

equal  to  25%  of  his  stock.  B  lost  $225.  A's  money  at 
that  time  is  twice  B's.  What  did  each  invest  ?  Ans.  : 
$600. 


PERCENTAGE,  15 


6.  I  sold  two  lots  for  $300  each.     On  one  I  gained  25%;  on 

the  other  I  lost  25  % .  How  much  did  I  lose  ?  What  per 
cent.?    Ans.  :  $40  loss;  dY/c, 

7.  I  sold  goods  at  a  gain  of  20%.     If  they  had  cost  me  $250 

more  I  would  have  lost  20%  by  the  sale.  What  did  the 
goods  cost  ?     Ans.  :  $500. 

8.  Isold  two  lots  for  $597,  gaining  by  the  sale  25%  on  the 

first  and  10%  on  the  cost  of  the  second.  If  |  of  the 
cost  of  the  first  equals  -|  of  the  cost  of  the  second,  what 
was  the  cost  of  each  ?    Ans.  :  ist,  $270  ;  2d,  $240. 

9.  If  I  sell  I  of  an  article  for  what  \  of  it  cost,  what  is  my 

gain  ^?    Ans.:  i6f^. 

10.  I  sell  goods  so  that  f  of  the  cost  is  received  for  \  of  the 

quantity  of  goods.     Find  gain  %.     Ans.  :  42f. 

11.  A  man  pays  |6oo  for  rent ;  f  of  this  sum  is  33^%  of  \  his 

income.     What  is  his  income?    Ans.  :  $2,700. 

12.  A  man  owning  33^%  of  a  farm  sold  25%  of  his  share  for 

$3350.50.  Whai  was  the  whole  farm  worth  ?  Ans.  : 
$40,206. 

13.  I  of  ^  of  60  is  75%  of  33^%  of  what  number?    Ans.:  20. 

14.  66f  %  of  I  of  100  is  5%  of  10  times  25%  of  what  number? 

Ans  :  213J. 

15.  A  man  paid  me  $80,  which  was  8^%  of  ^  the  amount  he 

still  owed  me.     How  much  does  he  still  owe  ?    Ans.  : 

$I,882yV 

16.  A  farm  cost  $3,000.     \  of  this  sum  was  62^%  of  what  the 

house  and  barn  cost.  Find  cost  of  house  and  barn. 
Ans.:  $1,600. 

17.  What  is  that  number  to  which,  if  37^%  of  \  of  20%  of  480 

be  added,  the  sum  will  equal  |  of  |  of  50%  of  324? 
Ans.:  27. 

18.  By  selling  a  cow  for  $21  I  lost  12^%.    At  what  price  should 

I  have  sold  her  to  have  gained  12^%?    Ans.  :  $27. 

19.  In  building  a  house  I  paid  3  times  as  much  for  material 

as  for  labor.  Had  I  paid  5%  less  for  material  and  4^ 
more  for  labor  the  house  would  have  cost  $2,334.  What 
did  it  cost  me  ?    Ans.  :  $2,400. 


i6  PERCENTAGE. 


20.  In  a  building  I  paid  three  times  as  much  for  material  as  I 

did  for  labor.  Had  I  paid  5%  less  for  material  and  4% 
more  for  labor  it  would  have  cost  me  $66  less.  What 
did  I  pay  for  the  labor  and  material?  Ans.  :  f6oo  and 
$r,8oo. 

21.  I  sold  a  carriage  to  B  and  gained  7^%.     B  sold  it  to  C  for 

$141.90  and  lost  12%.     What  did  it  cost  mc  ?   Ans.  :$  150. 

22.  A  hog  was  sold  for  75%  of  its  cost,  but  had  it  cost  me  $1  00 

more  it  would  have  sold  for  60%  of  its  cost.  Find  its 
cost.    Ans.  :  $4.00. 

23.  On  a  bill  of  $425,  what  is  the  difference  between  50%  off 

and  30  and  20%  off?    Ans.  :  $25;50. 

24.  A  buys  a  $60  sewing  machine  at  a  discount  of  30  and  i6|% 

off  and  sells  it  at  5%  above  the  list.  How  much  does 
he  make  ?     Ans.  :  $28. 

25.  I  bought  goods  amounting  to  $725.16  at  \  and  5  off.    What 

did  I  pay  for  them  ?    Ans.  :  $459.27. 

26.  I  of  what  I  received  for  an  article  is  equal  to  |  of  its  cost. 

What  is  the  gain  %?    Ans.  :  12^%. 

27.  I  marked  goods  to  gain  60%,  but  on  account  of  an  incor- 

rect measure  I  gained  only  40%.  What  was  the  length 
of  the  measure?     Ans.:  41^  in. 

28.  An  article  is  marked  to  gain  40%,  but  I  throw  off  \o%  and 

afterwards  pay  20%  for  collecting  the  debt.  What  is  my 
gain  or  loss?     Ans.:  |%  gain. 

29.  I  buy  vinegar  at   40  cts.  per  gallon.     I  then   add  water 

so  that  by  selling  the  mixture  at  30  cts.  per  gallon  I 
make  50% .     What  %  of  each  gallon  is  water?  Ans.  :  50% . 

30.  If  I  buy  for  20%  less  I  will  make  30%  more.     What  is  my 

gain  %?    Ans.:  20%. 

31.  If  f  of  the  selling  price  is  20^  less  than  the  cost,  what  is 

the  gain  or  loss?    Ans.:  6|%  gain. 

32.  66|^    of   240  is  ii^%  less  than    20%   of   what   number? 

Ans.  :  900. 

33.  If  f  of  the  selling  price  equals  f  of  the  cost  price,  find  the 

^  gain  or  loss.     Ans.  :  2of^  loss. 

34.  Two  houses  sold  for  $300  each.     On  one  I  gained  20;^  and 

lost  25%  on  the  other,  What  did  I  gain  or  lose  ?  Ans.  ; 
$50  loss. 


PERCENTAGE.  17 

35.  I  bought  a  watch  for  $30,  which  was  40%  less  than  its 

value,  and  sold  it  for  50%  more  than  its  value.  Find 
my  gain.    Ans.  :  $45. 

36.  I  sold  a  horse  at  a  gain  of  20% .    With  the  money  I  bought 

another  and  sold  it  for  $60  and  lost  37^%.  Find  my 
gain  or  loss.     Ans.  :  $16  loss. 

37.  If  an  article  had  cost  me  8%  less  my  gain  would  have  been 

15%  more.     Find  my  rate  of  gain.     Ans.  :  72^%. 

38.  I  bought  corn  at  50  cents  a  bu. ;  5%  wasted.    At  what  price 

must  I  sell  it  to  gain  33^%?    Ans.  :  7oi§c. 

39.  What  %  of  .005  is  $100?    Ans.  :  2,000,000%. 

40.  If  an  article  had  cost  me  10%  more  my  rate  of  ^ain  would 

have  been  20%  less.  What  is  my  rate  of  gain  ?  Ans.  : 
120%. 

41.  If  I  of  what  I  receive  for  a  horse  is  equal  to  |  of  its  cost, 

find  rate  of  gain.     Ans.:  \2.\%. 

42.  If  cost  had  been  20%  less,  loss  would  have  been  15%  less. 

What  was  the  loss  %?    Ans.  :  10%. 

43.  If  goods  cost  $180,  how  should  I  mark  them  so  that  I  may 

fall  10%  and  still  make  20%.     Ans.:  $240. 

44.  A,  B  and  C  are  partners.     A  receives  35%  of  the  profits. 

Of  the  remainder  B's  share  is  60%  more  than  C's.  C's 
income  is  increased  by  $150,  when  the  profits  rise  from 
10%  to  12%.  What  did  each  invest  ?  Ans.  :  A,  $10,500; 
B,  $[2,000  ;  and  C,  $7,500. 

45.  I  bought  a  number  of  lbs.  of  tea  for  $12.     If  I  had  bought 

10  lbs.  more,  I  would  have  been  allowed  a  discount  of 
10%  on  the  whole  and  the  price  would  have  been  $18. 
How  many  lbs.  did  I  buy  at  first  ?    Ans.  :  15  lbs. 

46.  I  lost  25%  on  the  purchase.    What  %  must  I  gain  on  the 

remainder  to  gain  25%  on  the  whole  ?    Ans.  :  66|%. 

47.  What  must  I  ask  for  a  hat  that  cost  $4  so  that  I  can  fall 

20%  an  1  still  make  20%  on  the  cost?    Ans.  :  $6.00. 

48.  A  and  B  have  $12,550;  A's  money  is  125%  of  B's  plus  $400. 

How  much  has  each  ?    Ans.  :  A,  $7,150;  B,  $5,400, 


i8  PERCENTAGE. 


49.  A  farmer  sold  two  horses  for  |8io,  receiving  f  as  much  for 

the  first  as  for  the  second.  On  the  jEirst  he  gained  33^%, 
and  on  the  second  he  lost  ii^fc.  What  did  he  gain? 
Ans.  :  I33.75. 

50.  I  bought  5  chests  of  tea  of  74  lbs,  each  at  45  cts,  per  pound 

at  2%  off  for  cash.  "What  will  be  my  profit  if  I  retail  it 
at  i2j%  advance?    Ans.:  $20.12. 

51.  If  my  horse  had  cost  25%  less  than  80%  of  what  he  did 

cost,  I  would  have  received  66f  %  more  than  I  did.  What 
%  did  I  gain  or  lose  ?    Ans.  :  iB^f  %  gain. 

52.  I  sold  two  horses  for  the  same  sum ;  on  one  I  gained  25%; 

on  the  other  I  lost  25%.  I  lost  $30.  Find  the  cost  of 
each?    Ans.:  $180,  first;  $300,  second. 

53.  I  bought  150  pounds  of  sugar  at  6  cts.;  after  selling  100 

lbs.  at  a  loss  of  5%,  at  how  much  a  pound  must  I  sell  the 
remainder  in  order  to  gain  10 fo  on  my  investment  ? 
Ans.  !  8 1  cts. 

54.  I  sold  my  goods  for  $1,125  5  ?  is  sold  for  25%  gain,  |  at  12^ 

^  gain,  and  the  remainder  at  ^  of  the  cost.  What  did 
I  pay  for  the  goods  ?    Ans.  :  $1,000. 

55.  What  is  the  difference  between  15%  and  5%  off,  and  5% 

and  15%  off?    7Vns.  :  o. 

56.  I  bought  an  invoice  of  goods  which  at  retail  sells  for  $850 

at  30%  off  and  2^%  oflf  for  cash.  What  did  they  cost? 
Ans.:  $580. i2|. 

57.  The  sum  of  two  numbers  is  4655,  and  40%  of  one  is  equal 

to  60%  of  the  other.  What  are  the  numbers?  Ans.: 
1862  and  2793. 

58.  A  teacher  spent  24%  of  his  money  and  had  $760.     What  is 

his  income  ?    Ans.  :  $1,000. 

59.  What  must  I  ask  for  a  hat  that  cost  $1.60  so  that  I  may 

reduce  my  asking  price  30%  and  lose  i2j%?  Ans.: 
$2.00. 

60.  I  bought  a  wagon  for  $72,  and  sold  it  for  25%  more  than 

it  cost  and  10%  less  than  I  asked.  What  was  my  asking 
price?    Ans.  :  $100. 

61.  i^%  of  my  money  is  12^%   more  than  $480.     How  much 

have  I  ?    Ans.  :  $36,000. 


PERCENTAGE. 


19 


A  sold  B  a  horse  for  $120.     If  B  had  paid  10%  less  A  would 
have  lost  8%.     What  did    the    horse    cost  A?    Ans.  : 


63.  I  sold  two  horses  for  $105  each  ;  on  one  I  gained  25%  and 

on  the  other  I  lost  25%.  Did  I  gain  or  lose?  How 
much  ?    Ans.  :  $14  loss. 

64.  I  pay  $600  a  year  for  rent ;  75%  of  this  is  just  33^%  of  \  of 

my  income.     What  is  my  income?    Ans.  :  $2,700. 

65.  I  own  J  of  a  vessel  and  sell  25%  of  it  for  $350;  at  that  rate 

what  is  the  whole  vessel  worth  ?    Ans.  :  $4,200. 

66.  I  bought  tea  for  20%  less  than  its  marked  value  and  got 

5%  off  for  cash.  I  sold  it  for  15%  above  the  marked 
value.     Find  ^  gain.    Ans.:  5ij%jc. 

67.  A  merchant  asked  25%  more  for  his  goods  than  they  cost 

him,  but  sold  them  at  10%  less  than  his  asking  price, 
realizing  $4684  profit.  What  was  the  cost  of  the  goods  ? 
Ans.:  $37,472. 

68.  I  sold  goods  at  a  gain  of  20%.     If  they  had  cost  me  $60 

less  I  would  have  gained  25%.  Find  cost  of  goods. 
Ans.  :  $1,500. 

69.  I  sold  two  houses  for  the  same  price  ;  on  one  I  gained 

25%  and  on  the  other  I  lost  25%.  I  lost  $60.  Find  the 
cost  of  each  house.     Ans.  :  $360  and  $600. 

70.  Sold  a  horse  at  a  gain  of  33^%  and  with  the  money  bought 

another  and  sold  it  for  $120  and  lost  25%.  What  was 
my  gain  or  loss  %?    Ans.  :  0%. 

71.  Bought  for  20^  off  and  sold  them  for  20%  above  list  price. 

I  gained  $90.     Find  the  cost.     Ans.  :  $225. 

72.  I  buy  goods  for  $1200  and  sell  ^  at  a  profit  of  15%.     I  then 

raise  the  price  from  15  to  17I  cts.  per  yd.,  and  sell  the 
remainder.     Find  my  profit.     Ans.  :  $190. 

73.  I  gained  30%  on  f  of  my  investment  and  lost  5%  on  the 

remainder.  My  profits  were  $720.  What  did  I  invest  ? 
Ans.:  $4,500. 

74.  I  sold  goods  and  gained  .^0%  on  |  and  lost  5%  on  |.    I  had 


I  sold  goods  and  gained  30%  on  |  and  lost  5^  on 
invested  $4500.     Find  my  gain.     Ans.  :  $405. 


i^  PEkCENTAGE. 


75.  I  bought  a  horse  for  $240.     What  must  I  ask  for  it  that  I 

may  deduct  25%  from  ray  asking  price  and  still  make 
25%?    Ans.:  I400. 

76.  I  bought  rice,  tea,  coffee  and  sugar.     The  tea  cost  60% 

more  than  the  rice;  coflPee  50^  more  than  the  tea; 
sugar  25%  more  than  the  coffee  The  whole  cost  was 
$240.  Find  the  cost  of  each.  Ans.  :  rice,  $30  ;  tea,  $48; 
coflfee,  $72 ;  sugar,  $90. 

77.  I  sold  \  of  my  goods  at  20%  gain,  and  the  remainder  at  a 

loss  of  10%;  my  gain  was  $100.  What  was  the  cost  of 
the  goods  ?    Ans.  :  $2,000. 

78.  A  farmer  sold  38%  of  his  land,  and  afterwards  bought  25% 

of  as  much  as  he  had  left.  He  then  had  9  acres  less 
than  at  first.    What  had  he  at  first  ?    Ans.  :  40  acres. 

79.  I  bought  300  yds.  of  cloth.     Sold  \  at  20%  gain,  and  the 

remainder  at  a  loss  of  \i\%.  My  whole  gain  was  $30. 
What  was  the  cost  of  the  cloth  per  yard  ?    Ans.  :  $2f . 

80.  I  sold  two  city  lots  for  $1200;  gained  20%  on  one  and  lost 

7.0%  on  the  other.  I  lost  $50.  What  did  each  cost  me  ? 
Ans.  :  I500  and  $750. 

81.  I  bought  sugar  at  8  cts.  alb.;  the  wastage  is  10^.     How 

must  I  sell  it  to  gain  30%?    Ans.  :  ii§  cts.  a  lb. 

82.  I  bought  a  barrel  of  wine  containing  46  gal.  at  $2.50  per 

gallon ;  if  6  gallons  leak  out,  how  must  I  sell  the  re- 
mainder to  gain  25%?    Ans.  :  $3.59!  per  gal. 

83.  Silver  is  y%  pure.    What  %  would  it  take  to  make  it  \\ 

pure?    Ans.:  if%. 

84.  Silver  is  \\  pure.    How  pure  would  it  be  if  vou  would  add 

2|%?    Ans.:  i|  pure. 

85.  The  cost  of  publishing  a  book  is  50  cts.  a  copy ;  if  the  ex- 

pense of  sale  be  10%  of  this,  and  the  profit  25%,  what 
does  it  sell  for  ?    Ans.  :  67^  cts. 

86.  My  retail  gain  is  33^%,  and  I  sell  at  wholesale  for  10% 

less  than  at  retail.  What  is  my  gain  ^  at  wholesale  ? 
Ans.:  20%. 

87.  Bought  dishes;  lost  15%  by  breakage;   at  what  %  above 

cost  must  I  sell  the  remainder  to  clear  20%  on  the 
whole?    Ans.:  4IxV 


PERCENTAGE. 


88.  If  I  pay  for  a  lb.  of  sugar,  and  get  a  lb.  troy,  what  %  do  I 

lose?    Ans.  :  25%. 

89.  Sold  my  lot  at  40%  gain  ;  with  the  proceeds  bought 
another  and  sold  it  for  $238,  losing  20%.  What  did  each 
lot  cost  me  ?    Ans.:  ist,  $21250;  2d,  I297.50. 

90.  I  spent  50%  of  my  money  the  first  day;  the  second,  50% 

of  the  remainder,  and  so  on  for  10  days,  when  I  had  left 
only  |i.oo.    What  had  I  at  first?    Ans.  :  |i,024. 

91.  I  made  this  year  $2400,  which  is  120%  of  my  gain  last,  and 

that  is  44f  %  of  my  gain  the  year  before.  What  were 
my  gains  the  two  previous  years  ?  Ans.  :  last  year, 
$2,000;  year  before,  $4,500. 

92.  I  bought  goods  by  dry  measure  and  sold  at  cost  by  wine 

measure  ;  I  bought  another  lot  of  same  by  wine  meas- 
ure and  sold  at  cost  by  dry  measure.  Required  the  rate 
of  gain  or  loss.     Ans.  :  2^f^yc  gain. 

93.  Bought  wheat,  and  6%  was  wasted  ;  30%  moulded,  which  I 

sold  at  40%  less  than  the  same  amount  cost ;  at  what  % 
advance  on  the  first  cost  must  the  good  wheat  be  sold 
so  as  to  yield  a  profit  of  14%  on  the  investment  ?  Ans.  : 
50%. 

94.  A's  money  is  3%  of  B's  and  4%  of  C's  ;  B  has  $100  more 

than  C.     How  much  has  A  ?    Ans.  :  $12. 

95.  If  25%  of  what  I  receive  for  an  article  is  gain,  what  is  my 
rate  of  gain  ?    Ans.  :  32,}  fc 

96.  I  sell  atSfo  gain  ;  I  invest  and  sell  again  for  12  J  %  gain  ; 
invest  again  and  sell  at  a  loss  of  4%,  and  have  $1,166.40. 
What  had  I  at  first  ?    Ans.  :  $1,000. 

97.  Henry  spent  iSf-y^  of  his  money,  and  then  received  $65  ; 

he  then  lost  75^  of  all  his  money,  and  had  $10  less  than 
he  had  at  first.     What  had  he  at  first  ?    Ans.  :  $33. 

98*  75%  of  the  difference  between  two  numbers  is  equal  to 
i6|  %  of  their  sum.  The  smaller  number  is  287.  Find 
the  larger.     Ans.:  451. 

I  bought  a  certain  number  of  hats  at  $2.50  each  ;  I  sold  f 
of  them  at  25%  profit,  and  on  the  sale  of  the  remainder 
I  lost  $15.  My  total  loss  was  equal  to  5%.  Find  the 
number  of  hats.    Ans.  :  120. 


22  PERCENTAGE. 


loo.  A  merchant  bought  loo  yds.  of  cloth  at  lo  francs  per 
yard.  \o%  was  lost  by  damage,  and  he  sold  the  re- 
mainder at  lo  marks  per  yard.  Find  the  rate  of  gain 
or  loss.     Ans.  :  9t¥3%  g^i^- 

loi.  A  has  50%  more  money  than  B.  E's  money  is  what  %  of 
A's  ?    Ans.  :  66|. 

102.  Sold  a  horse  at  a  profit  of  40%  on  the  cost,  and  at  a  dis- 

count of  12^%  from  the  asking  price.  What  was  my 
asking  price  if  cost  was  $100?    Ans.  :  $160. 

103.  10%  of  f  of  anything  is  what  ^  of  f  of  it?    Ans.  :  T%. 

104.  I  bought  cloth  and  marked  it  at  an  advance  of  40^.     In 

selling,  I  used  a  yard-stick  one  inch  too  short.  My  to- 
tal gain  was  $330.     Find  cost  of  cloth.    Ans.  :  $770. 

105.  A  buys  an  article  and  sells  it  to  gain   12^%.     If  he  had 

bought  it  for  10^  less  and  sold  it  for  $18  less  he  would 
have  gained  $20.     Find  the  cost.    Ans.  :  $i68f. 

106.  I  sold  a  piece  of  cloth  for  $24,  losing  25%.     If  I  had  sold 

it  for  $34,  would  I  have  gained  or  lost,  and  what  %? 
Ans.:    6J%  gain. 

107.  A  and  B  invested  equal  sums  in  business.    Againsasum 

equal  to  25%  of  his  stock  and  B  lost  $225,  when  A's 
money  at  this  time  was  double  that  of  B's.  What 
amount  did  each  invest  ?    Ans.  :  $600. 

108.  10%  of  120  is  8  less  than  5%  of  what  No.  ?    Ans.  :  400. 

109.  Sold  a  wagon  for  $25,  losing  i6f  ;^;  bought  another  ard 

sold  it  at  a  gain  of  16%.  I  neither  gained  nor  lost  on 
the  two.    What  did  each  cost.?   Ans.:  ist,$3o;  2d,|3[.2j. 

no.  By  selling  for  $5  less  than  cost  I  lose  \%.  Had  I  sold  i' 
for  $6  more  than  I  did  what  %  would  I  have  gained  ? 
Ans.:  4V %• 

111.  I  marked  goods  to  gain  60%,  but  on  account  of  using  an 

incorrect  yard- stick  I  only  gained  40%.  What  was  the 
length  of  the  measure  ?    Ans.  :  \\  yd. 

112.  I  buy  vinegar  at  $4  a  bl.  and  add  water  so  that  whea  I 

sell  it  at  $3  a  bl.  I  make  50%.  What  %  of  the  mixture 
is  water?    Ans.:  50%. 


INTEREST.  23 


.13.  Isold  goods  at  a  certain  gain  %.  If  they  had  cost  me 
50%  less  my  gain  would  have  been  6  times  as  great. 
What  %  did  I  gain  ?    Ans.  :  10%. 

114.  I  spent  equal  sums  for  rice,  coffee  and  tea.  I  gained  20% 
on  the  rice,  io%  on  the  coffee,  and  lost  8%  on  the  tea. 
My  total  receipts  were  $3,864.  Find  the  cost  of  each. 
Ans.:  $1,200. 


INTEREST. 


1.  I  gave  my  note,  10  per  cent,  from  date,  for  $2,442.04.    What 

sum,  paid  annually,  will  have  discharged  the  whole  at 
the  end  of  5  years?    Ans.  :  $644,204. 

2.  If  the  true  annual  rate  of  interest  be  10^,  what  would  be 

the  true  rate  for  each  73  days,  if  the  interest  be  com- 
pounded throughout  the  year  ?    Ans.:  1.924  per  cent. 

3.  I  get  24  cents  per  day,  which  is  f  of  a  mill  per  day  on  $1. 

How  much  have  I  at  interest?    Ans. :  $1,080, 

4.  I  pay  6%  int.  payable  semi-annually,  and  lend  it  at  12%, 

payable  quarterly.  I  clear  $2,450.85  a  year.  What  is  the 
sum?    Ans.:  $38,485.87. 

5.  A  debt  is  to  be  paid  in  4  equal  installments  at  4,  9,  12,  20 

months,  respectively;  its  cash  value  is  $750,  allowing 
5%  simple  interest.    What  is  the  debt?    Ans.  :  $785,156. 

6.  I  bought  a  lot  for  $156  due  in  8  months,  and  sold  it  at 

once  for  $180.    What  is  my  gain  %,  int.  ^\%  ?    Ans.: 

i8H%. 

7.  I  sell  my  farm  for  $4,850  ;  $250  payable  at  6  mon.,  i  J  yr., 

2\  yr.,  3^  yr.,  and  4^  yr.  each,  and  the  balance  in  5  yrs. ; 
if  money  is  worth  10%  per  annum  to  me,  what  is  the 
cash  value  of  the  sale?     Ans.:  $3,413.08-1-. 

8.  What  must  I  loan  Jan.  ist,  at  9% ,  to  be  repaid  by  5  install- 

ments of  $200  each,  payable  on  the  first  day  of  the  5 
succeeding  months?    Ans.  :  $978.15. 


24  INTEREST. 


9.  I  owe  $1500,  due  in  i  yr.  10  mo.  I  pay  $300  cash,  and  a  note 
for  6  mo.  for  the  balance  ;  what  is  the  face  of  the  note, 
interest  6%?    Ans.  :  |i, 080.56. 

13.  What  rate  do  I  make  by  charging  12%  per  annum,  com- 
pound interest,  payable  quarterly  ?    Ans.:  i2j%VWoV- 

II  What  is  my  gain  in  i  yr.,  on  $100  deposited  at  6%  and 
loaned  11  times  for  33  days.  Int.  2%  a  mon.?  Ans.: 
1 1 8. 20. 

i2o  Principal,  $3,325,  time  10  mo.  24  days.  Int.  $119.70;  find 
the  rate.    Ans.:  4%. 

13,  Ac  what  rate  per  annum  will  any  sum  double  by  simple 

interest  in  6  years  ?    Ans.  :  i6f  %. 

14,  At  what  per  cent,  will  $6,000  produce  $45  in  one  month  ? 

Ans.!  9%. 

15,  What  principal  will  produce  $17  interest  in  68  da.  at  1%  a 

month.?    Ans.:  $750. 

Lo.  At  what  rate  per  annum  will  any  sum  treble  itself  at  sim- 
ple interest  in  30  yrs.  ?    Ans.  :  6f  %. 

17.  What  is  the  rate  of  interest  when  stock  bought  at  40% 

discount  yields  a  semi-annual  dividend  of  5%?    Ans.: 

i6|f.. 

18.  At  what  rate  per  annum  will  any  sum  quadruple  itself  at 

simple  int.,  in  24  yrs.  ?    Ans.  :  12^%. 

19.  What  sum,   drawing  simple  int.  at  5%   per  annum,  will 

amount  to  $819.45  in  i  yr.  8  mo.  5  da.  ?    Ans.  :  $755.93. 

20.  In  what  time  will  $100  double  itself  by  simple  interest  at 

8%?    Ans.:  12J  yrs. 

21.  The  interest  on  twice  A's  and  3  times  B's  money  for  5  yrs. 

6  mo.  at  6%  is  $2,640;   how  much  has  each  if  twice  A's 
equals  3  times  B's?    Ans.:  A,  $2,400;  B,  $1,600. 

22.  How  long  must  I  deposit  $1,37450,  at  10^^,  to  pay  a  debt 

of  $1,480.78?     Ans.  :  9  mo.  8^— da. 

23.  How  long  would  it  take  $175.12  to  produce  $6.43,  interest 

6%?    Ans.:  7  mo.  10  da. 

24.  How  long  will  it  take  $3,642.08  to  amount  to  $4,007.54  at 

i2'i^?    Ans.:  10  mo.  i  da. 


INTEREST.  25 


25.  What  is  the  rate  of  discount  when  a  60-day  note  yields  2% 

interest  a  mouth?    Ans.  :  "^.^iz-hfo- 

26.  Find  the  face  of  a  90-day  note,  to  net  |i,ooo  when  dis- 

counted at  6^.    Ans.  :  $1,015.74. 

27.  At  what  rate  should  I  discount  a  60-day  note  to  get  20% 

per  annum  interest ?    Ans.:  19/07% - 

28.  What  is  the  rate  when  the  interest  on  $200  for  2  years  is 

$48?    Ans.:  12%. 

29.  How  much  must  I  loan  at  6%  to  produce  $48  in  2  yrs.  ? 

Ans.:  $400. 

30.  I  invest  \  of  my  annual  income  in  mortgages  paying  6% 

annual  interest.  In  6  mo.  12  days  my  interest  from 
them  was  $640.  What  is  my  annual  income  ?  Ans.  : 
$100,000. 

31.  Find  the  difference  between  the  annual  and  compound 

interest  of  $400  for  2  yrs.  at  8%  ,    Ans.  :  o. 

32.  Find  the  difference  between  the  annual  and  compound 

interest  of  $200  for  3  yrs.  at  6%,    Ans. :  $04+. 

33.  Find  the  difference  between  the  simple  and  compound 

interest  of  $200  for  2  yrs.  at  8% ,     iiNe. "  li  28 

34.  What  must  I  save  annually  commencing  at  18,  so  that  I 

may  have  $25,000  when  I  am  37  yrs.  of  age  if  I  get  6% 
compound  interest?    Ans.  :  $698,744-. 

35.  If  the  interest  on  the  sum  of  A's  and  B's  money,  for  3  yrs. 

9  mo.,  at  8%,  is  $3,213,  and  |  of  A's  money  is  equal 
to  \  of  B's,  how  much  has  each  ?  Ans.  :  A,  $5,680 ;  B, 
$5,040. 

36.  \  of  the  cost  of  A's  house,  increased  by  \  of  the  cost  of 

his  farm  for  2  yrs.  at  5%  amounts  to  $4,950.  What  was 
the  cost  of  each  if  \  of  the  cost  of  the  house  was  only 
f  as  much  as  f  of  the  cost  of  the  farm  ?  Ans.  :  House, 
$r,666.66|;  farm,  $4,375. 

The  sum  of  f  of  A's  plus  \  of  B's  money  being  on  interest 
for  8  yrs.  at  6%  gives  $960  interest.  What  has  each  if  \ 
of  B's  is  3  times  |  of  A's  ?    Ans.  :  A's,  $750;  B's,  $3,000. 

A's  money  added  to  \  of  B's,  which  is  to  A's  as  2  to  3, 
being  put  on  interest  for  6  vrs  ,  at  4% ,  amounts  to  $744. 
What  has  each  ?    Ans.  :  A,  $360;  B,  $360. 


26  INTEREST. 

39.  In  what  time  will  $13  at  6%  give  $0,975  interest?    Ans. :  i 

yr.  3  mo. 

40.  The  interest  of  $325   for  2  mo.  is  $3.25.     Find  the  rate. 

Ans.:  6%. 

41.  By  lending  a  sum  of  money  at  4%  and  another  sum  at  5% 

the  total  interest  is  $68.  If  the  rates  are  changed  the 
interest  is  $67.  Find  the  principal  lent  at  each  rate. 
Ans.  :  $700  and  $800. 

42.  The  interest  on  my  money  for  9  mo.  at  5%  is  $150  less  than 

the  same  for  15  months  at  4%.  Find  the  sum.  Ans.  : 
$12,000. 

43.  A  sum  of  money  doubled  itself  in  16  yrs.  at  simple  inter- 

est.    Find  the  rate.     Ans.  :6^%. 

44.  The  amount  of  a  certain  sum  at  simple  interest  for  3  yrs. 

is  $558  ;  for  4^  yrs.  it  amounts  to  $612.  Find  the  rate  and 
principal.     Ans.  :  Rate,  8%;  prin.,  $450. 

45.  The  interest  is  |  of  the  principal,  and  the  difference  be- 

tween the  interest  and  principal  is  $120.  Find  the  in- 
terest.    Ans.:  $80. 

46.  The  interest  is  \  of  the  principal.     The  difference  between 

the  interest  and  principal  is  $120.  Find  the  principal. 
Ans.  :  $150. 

47.  The  interest  on  a  sum  of  money  in  5  yrs.  is  f  of  the  sum. 

What  is  the  rate  ?    Ans.  :  \2\%. 

48.  At  3^%  for  8  yrs.  what  fraction  of  the  principal  is  \  of  the 

interest.    Ans.:  2V 

49.  The  interest  of  a  sum  of  money  at  the  end  of  15  yrs.  was 

f  of  the  sum  itself.     What  was  the  rate  ?    Ans.  :  4%. 

50.  A  sum  of  money  in   9  yrs.   at   11%    at   simple  interest 

amounts  to  $597.  In  how  many  years  will  it  amount  to 
$663  ?    Ans.  :  1 1  years. 

51.  The  interest  of  $1,460  for  one  day  is  25  cents.     Find  the 

rate  %  per  annum  (365  da.)     Ans.  :  6^fc. 

52.  In  what  time  at  simple  interest  will  $723. 16 J  return  |  of 

itself  at  7^%?    Ans.  :  8  yrs.  4  mo. 

53.  A  certain  sum  in  8  months  amounts  to  $790,  and  in  19 

months  to  $845.     What  is  the  rate  ?    Ans.  :  Sfo, 


STOCKS  AND  BONDS. 


5  1.   What  is  the  difference  between  the  simple  interest  of  $139 
for  600  days  and  $600  for  139  days  ?     Ans.  :  o. 


55.    The  interest  of  a  certain  sum  is  \  of  tlic  principal.     The 
amount  is  $640.     Find  the  principal.     Ans.  :  $560. 

5O    At  what  rate  simple  interest  will  a  sum  become  4  times 
itself  in  20  yrs.  ?    Ans.:  15%. 


STOCKS  AND  BONDS. 


What  do  I  receive  for  32  shares  of  telegraph  stock  which 
a  broker  sells  for  me  at  15%  discount,  charging  \'fo 
brokerage?    Ans.  :  $2,712. 

I  purchased  18  shares  of  telegraph  stock  for  $500  per  share 
at  a  premium  of  2%  and  sold  them  for  28^  below  par. 
What  was  my  loss  ?     Ans.  :  $2,700. 

How  many  shares  of  stock  must  be  sold  at  4%  discount, 
brokerage  ifo,  to  realize  $4,775?    Ans.  :  50. 

i  received  a  6%  dividend  on  certain  stock  and  invested 
the  money  in  the  same  stock  at  75%.  My  stock  had 
then  increased  to  $16,200.  What  was  the  amount  of  my 
dividend  ?     Ans.  :  $900. 

If  I  buy  6%  stock  at  90%,  what  rate  of  interest  do  I  re- 
ceive on  my  investment  ?    Ans.  :  6|%. 

At  what  rate  must  an  8^  stock  be  purchased  to  yield  the 
purchaser  7%  interest?    Ans.  :ii4f. 

At  what  price  must  6%  stock  be  purchased  in  order  to  ob- 
tain Sfc  income  on  the  investment?    Ans  :  75%. 

What  sum  must  be  invested  in  8%  stock  at  130  to  produce 
an  income  of  $2,000  ?    Ans.  :  $32,500. 

Sought  120  shares  of  canal  stocks,  $10  each,  at  j\%  ad- 
vance and  sold  at  §%  discount.    Find  my  loss.    Ans.  :  $23. 


28  STOCKS  AND  BONDS. 


10.  ^.t  what  discount  must  I  buy  stocks  so  that -by  selling  at 

2%   premium    I    may   gain    20%    on    my   investment? 
Ans.  :  15%. 

11.  If  I  receive  an  annual  dividend  of  6%  on  Michigan  stock, 

which  cost  me  but  37^%,  what  %  income  do  I  receive 
on  my  investment?    Ans.  :  16%. 

12.  I  bought  bonds  at  4%  discor.nt  and  sold  them  at  5%  pre- 

mium.    I  gained  $450.     How  many  shares  of  $50  each 
did  I  buy  ?    Ans.  :  100. 

13.  When  N.  Y.  Central  is  quoted  at  %|,  how  much  stock  can 

be  bought  for  $6,894,  brok.  J%?    Ans.  :  $7,200. 

14.  I  buy  stocks  at  25%  below  par  and  r,ell  20%  above  par. 

What  %  do  I  make  ?    Ans.  :  60^. 

15.  If  I  buy  stock  at  30%  discount  and  every  6  months  re- 

ceive a  dividend  of  4^,  what  is  my  annual  rate  of  inter- 
est?   Ans.:  iif%. 

16.  A  person    exchanged  250  shares  of  6%  bonds  at  70,  for 

bonds  bearing  8%  at  120.    What  is  the  difference  in  his 
income  ?     Ans.  :  $333^. 

17.  How  many  shares  of  stock  $100  each  must  be  sold  at  4% 

discount,  brok.  ^%,  to  realize  $4,775.     Ans.  :  50. 

18.  My  broker  sells  50  shares  of  stock,  brok.  J%.     He  remits 

me  $2,348.20.    At  what  rate  did  the  stock  sell?    Ans.: 

19.  At  what  price  must  I  purchase  15%  stock  that  it  may  yield 

the  same  income  as  6%  stock  purchased  at  90.     Ans.  : 
225. 

20.  If  stock  bought  at  15%  premium  pays  8%  on  the  invest- 

ment, what  %  would  it  pay  if  bought  at  10%  discount? 
Ans.:  iof%. 

21.  What  should  I  pay  for  a  6%  bond  of  $50  that  I  may  realize 

8%?    Ans.  :  $37-50. 

22.  When  gold  is  at  115  and  U.  S.  ia-40's  at  105,  what  is  a  $500 

bond  worth  ?    Ans.  :  $456.52/3. 

23.  A  party  investing  in  5%  bonds  realizes  8%  income  on  his 

investment.     How  did  the  bonds  stand?    Ans. :  62^. 

24.  How  much  must  be  invested  in  U.  S.  8's  at  95  to  receive 

an  annual  income  of  $3,000?    Ans.  :  $35,625. 


» 


STOCKS  AND  BONDS.  29 

-25.  What  %  on  his  investment  will  a  person  receive  who  buys 
f  U.  S.  6's  at  107  when  gold  stands  at  150  ?    Ans.  :  8j%\%. 

26.  When  gold  is  worth  129  what  yearly  %  income  will  a  per- 

son receive  Who  invests  $7,540  in  U.  S.  6's  when  selling 
at  104?    Ans.:  7|f%. 

27.  What  must  gold  sell  for  that  a  party  investing  in  5^40's  at 

105  may  realize  8%  on  his  investment  ?    Ans.  :  140. 

28.  When  gold  is  at  115  what  is  the  semi-annual  interest  in 

currency  on  $9,500  in  io-40's  ?     Ans.  :  $273,125. 

29.  When  gold  is  at  115  what  amount  in  currency  can  be 
bought  for  $8,500  in  gold  ?    Ans.  :  $9,775- 

A  broker  invested  $21,300  in  5-20's  at  106J  and  sold  them 
at  109.     How  much  did  he  gain  ?    Ans.  :  $500. 

31.  When  gold  is  105  what  is  the  value  in  gold  of  a  dollar  in 
currency?    Ans.  :  95/x  *^^^^®' 

32.  Bought  $800  in  gold  at  no,  brok.  1%.     What  did  I  pay  for 

gold  in  currency  ?    Ans.  :  $881. 

33.  What  face  value  of  stock  paying  if  %  quarterly  dividend 

will  yield  an  annual  income  of  $513.50?    Ans.  :  $7900. 

34.  What  must  be  invested  in  6\%  bonds  bought  at  105  to 

realize  an  income  of  $1,000?    Ans.  :  $16,153.84x^3. 

35.  At  the  end  of  6  mos.  I  received  4%  dividend  in  stock;  at 

the  end  of  the  year,  a  5%  dividend  in  stock.  I  then 
had  $12,012  worth  of  stock.  How  many  shares  had  I  at 
first?    Ans.:  no. 

36.  When  U.  S.  4's  are  worth  106,  what  will  be  my  yearly  in- 

come in  gold  from  bonds  that  cost  $4,982  ?    Ans.  :  $188. 

37.  If  I  pay  70  for  bonds  that  yield  an  annual  income  of  7%, 

what  %  do  I  get  on  my  investment?    Ans.  :  10%. 

38.  How  many  shares  of  railroad  stock  bought  at  95^  and  sold 
I  at  105.  brokerage  i^%  on  each  transaction,  will  yield  an 
'  annual  income  of  $925  ?    Ans.  :  100. 

39.  What  must  I  invest  in  U.  S.  5's  at  118  to  yield  an  annual 

income  of  $1,921  in  currency  when  gold  is  worth  113  ? 
Ans  :  $40,120. 


3o  STOCKS  AND  BONDS.  i 

40.  I  own  25  shares  in  an  electric  light  plant  which  declares  ' 

a  5%  annual  dividend.  I  take  the  dividend  in  lighting  ; 
at  the  rate  of  $2.50  per  lamp.  How  many  lamps  can  I  j 
burn  10  mos.  of  each  year  ?    Ans.  :  60.  i 

41.  What  will  be  the  cost  of  25  $1,000  5-20  U.  S.  bonds  of  1865  , 

at  1 14^,  brokerage  J%?    Ans.:  $28,593.75.  ! 

42.  My  broker  sells  a  certain  amount  of  stocks  and  remits  me  ] 

$25,734.37 J.  His  brokerage  at  yV%  was  $15.62^.  What  j 
was  the  price  of  the  stocks  ?    Ans.  :  103.  ' 

43.  What  is  my  currency  income  if  I  invest  $5,220  in  U.  S.  5-20  i 

6fo  bonds  at  116  when  gold  is  105?    Ans.  :  $283.50.  j 

44.  Find  the  cost  of  125  shares  U.  P.  R.  R.  stock  at  68^,  brok-  \ 

eragei%?    Ans.:  $8,593.75.  j 

45.  What  will  $8,000  U.  S.  io-40's  of  '65  cost  at  108^^,  brok.  J%? 

Ans.  :  $8,670.  • 

46.  How  much  will  55  shares  of  railroad  stock  cost  at  28|, 

brok.  $13.75?    Ans.:  $1,595-  j 

47.  If  I  pay  $5,418.75  for  50  U.  S.  5-20's  at  8J%  premium,  what 

is  the  rate  of  brokerage?    Ans.  :  i%.  j 

48.  Bought  35  shares  of  canal  stock  at  86J  and  sold  them  at  \ 

8i%  premium.    Find  my  gain.    Ans.  :  $761.25.  | 

49.  I  sold  135  shares  of  stock  at  a  discount  of  i$\%,  paying  , 

\%  brokerage.     How  much  did  I  receive  for  it  ?    Ans.  :  ■ 

$11,407.50.  ^ 

50.  How  many  shares  of  bank  stock  at  5%  discount  can  be  1 

purchased  for  $3,790  if  \%  is  paid  for  brokerage?  Ans.  :  ! 
40.  i 

51.  What  will  be  my  income  if  I  invest  $4,196.25  in  5%  stock  \ 

purchased  at  93,  allowing  \fc  for  brokerage  ?   Ans.  :  $225.  \ 

52.  What  will  be  my  annual  income  if  I  invest  $1,299  ^^  ^%    i 

stock  purchased  at  37^,  allowing  \%  brokerage.  Ans.:  i 
$209,234-.  ; 

53.  If  I  receive  $622.80  by  investing  $4,696.95  in  bonds  at  45%,   ' 

brokerage  \%^  what  rate  do  the  bonds  bear  ?    Ans.  :  6%.  [ 

54.  Which  is  more  profitable,  and  how  much,  to  invest  $5.':;j)0  1 

in  6%  stock  purchased  at  75,  or  5%  stock  purchased  al  ■ 
60%?    Ans.:  5^  at6oby  $i6.66f. 


I 


STOCKS  AND  BONDS.  31 


55.  U.  S.  5-20's  pay  6%  iuterest  iu  gold.     What  will  be  my  in- 

come in  currency  by  investing  $11,212.50  at  112J  when 
gold  is  at  106P    Ans.  :  $641.25. 

56.  Which  is  more  profitable,  to  buy  6%  bonds  at  90,  interest 

payable  in  currency,  or  5%  bonds  at  95,  interest  payable 
in  gold,  when  gold  is  at  io6|  ?     Ans.  :  6%  at  90. 

57.  Which  affords  the  greater  %  of  income,  bonds  bought  at 

125  which  pay  8%,  or  bonds  which  pay  6%  bought  at  a 
discount  of  10% ?    Ans.  :  6%  at  10%  discount. 

^  58.   Which  is  more  profitable,  and  how  many  % ,  to  buy  New 
'  York  7's  at  105,  or  Louisiana  6's  at  98  ?    Ans.  :  N.  Y.  7's 

59.  What  must  I  pay  for  stock  which  pays  a  dividend  of  15  fo 

so  that  I  may  realize  7%  on  my  investment  ?    Ans.  :  2i4f. 

60.  I  bought  stock  at  225  which  yielded  the  same  income  as 

6%  stock  bought  at  90%.     What  rate  did  my  purchase 
bear?    Ans.:  15^. 

61.  I  sold  $5,000  of  U.  S.  6's  of  '81  at  115  and  invest  in  io-40's 

at  105.     Do  I  gain  or  lose  and  how  much  annually  (lat- 
ter bearing  5%)?    Ans.  :  $26.20  loss. 

62.  What  is  a  dollar  in  currency  worth  wh^n  gold  is  quoted 
at  125  ?    Ans.  :  80  cents. 

63.  If  stock  bought  at  105  pays  6%  on  the  investment,  what 
will  it  pay  if  bought  at  15%  discount?    Ans.:  7tV%- 

64.  What  must  be  the  price  of  gold  so  that  a  person  investing 

in  5-20's  at  108  may  realize  7% ?     Ans.  :  126. 

65.  If  I  invest  a  certain  sum  in  6's  at  85  and  the  same  in  7's  at 

95  and  receive  $5  more  a  year  from  the  latter  investment, 
how  much  do  I  invest  in  each  ?    Ans.  :  $1,615. 

66.  What  sum  must  I  invest  in  U.  S.  5-20's  of  '82  at  96!%, 

brokerage  |%,  to  secure  an  annual  income  of  $1,500? 

Ans.  :  $24,250. 

67.  If  I  invest  $10,200  in  U.  S.  6's  at  30%,  what  is  my  income  ? 

Ans.  :  $2,040. 

68.  If  I  pay  125  for  10%  bonds,  what  %  do  I  make  ?    Ans.  :  Sfc, 

69.  When  gold  is  50%  premium  over  paper  money,  what  is  a 

paper  dollar  worth  ?    Ans.  :  66f  cents. 


32  STOCKS  AND  BONDS. 

70.  At  what  price  will  a  ^^Q%  government  bond  of  $1,000  pay 

the  purchaser  6%  interest  ?    Ans.  :  I2i|. 

71.  At  what  price  will  a  10%  bond  of  $50  pay  9%  interest? 

Ans.  :  $55f  • 

72.  If  gold  were  worth  125  and  U.  S.  5-20's  worth  105,  what 

size  of  bond  could  I  buy  for  $420  in  gold  ?    Ans.  :  $500. 

73.  I  pay  $150  for  two  6%  bonds  of  $100  each.     What  rate  do 

I  realize  on  the  investment  ?    Ans.  :  8^ . 

74.  I  pay  through  a  broker  $29,840  for  6%  Cleveland  Water 

Works  bonds  at  93^  % ,  including  brokerage.  The  owner 
afterwards  refunds  the  brokerage,  $240.  What  rate  do 
I  realize  on  the  investment?     Ans.  :  d^-fc. 

75.  I  have  $8,475  invested  in  U.  S.  io-40's  at  113.     What  is  my 

semi-annual  income  in  currency,  gold  being  worth  no? 
Ans.:  $206.25. 

76.  When  gold  is  worth  128,  what  half-yearly  income  in  cur- 

rent funds  will  a  person  receive  who  invests  $7,540  in 
U.  S.  ia-40's  when  selling  at  104  ?    Ans.  :  $232. 

77.  What  %  on  my  investment  will  I  make  by  buying  U.  S. 

7iV's  at  104  ?    Ans.  :  ^i^. 

78.  What  must  gpld  sell  for  that  a  party  investing  in  U.  S.  6's 

may  realize  8% ?    Ans.  1133^. 

79.  My  semi-annual  interest  in  currency  is  $276  on  $9,600  U. 

S.  bonds  when  gold  is  at  115.  What  rate  do  the  bonds 
bear?    Ans.:  5%. 

80.  When  gold  is  at  115,  what  amount  in   currency  can  be 

bought  for  $8,500  in  gold  ?    Ans.  :  $9,775. 

81.  A  broker  invested  $26,250  in  5-20's  at  106.V  and  sold  them 

at  109.     How  much  did  he  gain?    Ans.  :  $616.19-!-. 

82.  Bought  $8,000  in  gold  at  no,  brok.  \fc.    What  did  I  pay 

in  currency?    Ans.:  $8,810. 

83.  Bought  stock  at  20^  discount,  sold  out  at  112,  realizing 

$2,240.     What  did  I  invest?    Ans.  :  $1,600. 

84.  When  gold  is  at  a  premium  of  25%,  what  is  the  discount 

on  greenbacks ?    Ans.:  20%. 

85.  What  income  will  be   obtained   by  investing  $6,840  in 

stocks  bearing  6%  interest  at  95  ?    Ans.  :  $432. 


STOCI^S  AND  BONDS.  33 

86*  U.  S.  5-20's  pay  interest  in  gold.  What  will  be  my  in- 
come in  currency  by  investing  $11,212.50  at  ii2j^wlien 
gold  is  at  a  premium  of  6^  ?    Ans.  :  $641.25. 

87.  Bonds  at  20^  premium,  brokerage  |%,  cost  $300.87 J  more 
than  their  face.  What  was  the  face  of  the  bonds? 
Ans.  :  $i,458ff. 

88.  A  owned  .075  of  all  the  stock  of  a  bank.  The  stock  in- 
creases .015  the  first  year.  The  increase  was  invested 
in  stock.  He  gave  his  son  .025  of  all  the  stock  then 
owned  by  him.  What  %  of  the  whole  stock  of  the  bank 
did  he  give  away  ?     Ans.  :  .001875= j\%. 

89.  Bought  a  check  at  55%;  traded  it  for  canal  stock  at  60%, 
which  bears  7%  interest.  What  %  interest  do  I  receive 
on  my  investment ?    Ans.:  21/^%. 

90.  I  invested  $2,700  in  bonds  at  25%  discount,  which  pays  8%. 
How  much  must  I  invest  in  bonds  at  4%  discount  and 
paying  10%  dividend  to  secure  an  equal  income.?  Ans.: 
$2,764.80. 

91.  I  sold  canal  stocks  at  a  loss  of  15%.  I  invested  the  pro- 
ceeds in  R.  R.  stocks  and  sell  at  15%  gain.  Do  I  gain 
or  lose  on  the  two  speculations?     How  many  %?    Ans.: 

2\%  loss. 

92.  Bought  bonds  at  lofo  discount,  which  rose  to  5%  pre- 
mium, and  sold  for  cash.  After  paying  a  debt  of  $33, 1  in- 
vested the  remainder  in  stocks  at  102,  which  at  par  left 
me  $11  less  than  at  first.  How  much  had  I  at  first? 
Ans.:  $148.50. 

93.  I  buy  bonds  at  94 ;  sell  at  100 ;  my  gain  is  $666 ;  how  many 

$50  shares  ?    Ans.  :  222. 

94.  I  exchanged  72  N.  Y.  bonds  ($1,000  each)  at  6\%  premium 

for  Ky.  bonds  ($500  each)  at  2%  premium.     How  many 
of  the  latter  did  I  get  ?    Ans.  :  150. 

195.  4%  canal   stock  brings  an  income  of  $300,  but  sells  in 
market  for  92%.    What   amount  is  invested?    Ans.: 
$6,900. 
I 


96.  I  invested  in  5%  furnace  stock  at  75.  My  income  is  $180. 
How  much  must  I  invest  in  6%  state  stock  at  102  to 
have  the  same  income  ?    Ans.  :  $3,060. 


34  STOCKS  AND  BONDS. 

97.  Which  is  the  better  investment,  canal  4's,  registered  at 

99f,  or  U.  S.  4i's  at  106.     Ans.  :  Latter  ^^^%  better. 

98.  What  is  the  value  of  18  shares  R.  R.  stock  ($75  each)  at  8% 

discount?    Ans.  :  $1,242. 

99.  What  must  be  paid  for  fifteen  $100  shares  of  mining  stock 

at  18%  advance  ?     Ans.  :  $1,770. 

ICO.  How  much  money  must  I  give  with  nine  $100  shares  at 
15%  discount  in  exchange  for  eight  $100  bonds  at  2% 
discount  ?     Ans.  :  $19. 

loi.  How  many  $50  shares  at  8%  discount  must  be  given  for 
23  bonds  of  $100  each  at  2%  premium  ?    Ans.  :  51. 

102.  I  bought  18  shares  of  $50  each  at  J%  discount  and  sold  at 

f  %  premium.    What  is  my  gain  ?    Ans.  :  $11.25. 

103.  Bought  120  shares  of  R.  R.  stock  ($10  each)  at  i\%  ad- 

vance and  sold  at  1%  discount.  Find  my  loss.  Ans.: 
$23. 

104.  I  bought  stock  at  65  and  after  receiving  a  dividend  of 

S\%  sold  it  at  82  and  made  $1,125.  How  much  stock 
had  I  and  what  %  did  I  realize  ?  Ans.  :  50  shares ; 
realized  22 J%. 

105.  I  bought  stock  at  73,  and  then  received  $945  as  a  dividend 

at  2j%,  when  I  sold  my  stock  at  86|.  How  much  stock 
had  I  and  what  did  I  make  ?  Ans.  :  420  shares  ;  made 
$6,510. 

106.  I  bought  $9,040  worth  of  stock  at  $113,  and  after  receiv- 

ing a  dividend  of  5^%,  sold  at  in  J.  How  much  did  I 
make  and  how  much  stock  did  I  buy  ^  Ans.  :  Made 
$320;  had  $8,000  stock. 


DISCOUNT.  35 


DISCOUNT. 


What  sum  is  it  whose  true  discount  by  simple  interest  for 
4  yrs.  is  $25  more  at  6%  than  at  4%  per  annum  ?  Ans.  : 
$449.50. 

2.  I  bought  a  lot  for  $156  due  in  8  months,  and  sold  it  at  once 

for  $180.    Find  my  gain  %,  int.  4^%.    Ans.  :  i2^ii^%, 

3.  If  I  discount  a  note  at  20%  per  annum  I  make  22^%  inter- 

est per  annum ;  how  long  does  the  note  run  ?  Ans.  : 
200  da. 

4.  I  discount  a  6  mos.  note  at  |%  a  month  and  it  yields 

$4,800.    What  was  its  face  ?    Ans.  :  $5,057.06+. 

5.  Paid  $180  for  a  claim  due  in  6  mo.     A  broker  bought  the 

claim  same  day,  taking  bank  discount  at  6%.  I  cleared 
$13.90.     What  was  the  amount  of  the  claim.    Ans.  :  $200. 

6.  The  true  discount  on  a  sum  for  3  yrs.  4  mo.  at  2  J  %  is  $60 ; 

and  the  interest  on  the  same  sum  for  the  same  time 
and  rate  $65.  Find  the  principle  and  rate.  AnS.  :  $780 
prin.;  |f%  rate. 

7.  How  long  must  a  note  run  discounted  at  8%  to  yield  9^ 

per  annum .?    Ans.  :  i  yr.  4  mo.  20  da. 

8.  The  true  discount  of  a  debt  of  $405  due  in  10  mo.  20  da.  is 

$30.    What  is  the  rate  ?    Ans.  :  9%. 

9.  Sold  flour  for  $3,275.60,  half  cash,  the  balance  a  note  at  60 

days.  If  the  note  is  discounted  in  bank  at  10%,  what 
will  be  the  net  proceeds  of  the  sale  ?    Ans.  :  $3,272.83-}-. 

Sold  50  bl.  of  rum,  each  containing  31  gal.  2  qt.,  at  $2.40 
a  gal.,  receiving  a  note  at  90  da.  What  would  be  the 
proceeds  of  this  note  discounted  at  7j%?  Ans.; 
$3,706.76+. 

What  will  be  the  proceeds  of  a  note  of  $999,  payable  in 
97  days,  int.  8% ?    Ans.:  $977.27. 


36  DISCOUNT. 


12.  The  discount  of  a  certain  sum  at  6%  for  i8o  days  was 

$185.49.  What  would  have  been  the  true  discount? 
Ans.  :  $180. 

13.  The  present  worth  is  $326,40,  true  discount  $114.24,  time 

7  yrs.  9  mo.  10  da.     Find  the  rate.     Ans.  :  \Yfc. 

14.  A  bank  paid  $336.43  for  a  note  of  $340  discounted  at  6^. 

How  long  did  the  note  run  ?    Ans.  :  60  days. 

15.  The  discount  on  a  debt  due  in  2  yrs.  was  $45.    What  would 

have  been  the  discount  on  the  same  note  10  months  be- 
fore due  ?     Ans.  :  $26^^. 

16.  The  discount  was  $3.96  on  a  note  of  $396  for   57  days. 

What  was  the  rate  of  discount?    Ans.  :  6^. 

17.  Find  the  true  discount  of  a  debt  of  $405  due  in  10  mo.  20 

da.  at  9%.     Ans.:  $30. 

18.  The  bank  discount  of  a  note  of  $750  was  $8.50.     What  was 

the  time,  interest  8% ?    Ans.  :  48  days. 

19.  What  is  the  present  worth  of  a  debt  due  in  4  yrs.  8  mon 

10  da,,  the  true  discount  at  6%  being  $169  ?    Ans.  :  $600, 

20.  The  bank  charged  $33.20  and  paid  $2,366.80  for  a  note  dis 

counted  at  6%.  How  long  had  it  to  run  ?  Ans.  :  2  mo 
20  da. 

21.  Rate  8%,  discount  $105,  debt  $245.     Find  the  time.    Ans. 

9  yrs.  4  mo.  15  da. 

22.  I  received  $792  for  a  note  of  $800  payable  in  42  days.    Find 

the  rate.     Ans.:  8%. 

23.  A  bank  gave  $1,385.30  for  a  note  payable  in  60  da.     How 

much  did  they  charge  for  discounting  at  6%  ?  Ans.. 
$14.70. 

24.  A  bank  charged  $27.30  for  discounting  a  note  of  $2,600, 

payable  in  sixty  days.     Find  the  rate.     Ans  :  6%. 

25.  The  bank  discount  on  a  note  having  2  mos.  to  run  was 

$72.66,  int.  (i%.     Find  the  face.     Ans.:  $6,920. 

26.  The  proceeds  of  a  note  dated  Feb.  19th,  1892,  payable  Jan. 

ist,  1893.  and  bearing  8%  int.,  was  $105. 51J,  when  dis- 
counted Oct.  12th,  1892,  at  6%.  What  was  the  face  of 
the  note  ?     Ans.  :  $100. 


DISCOUNT. 


27.  For  what  sum  must  I  give  my  note  for  6  mos.  to  realize 

$1,500;  int.  10^?    Ans.  :  $1,580.33. 

28.  What  is  the  present  worth  and  discount  at  8%  of  a  note  of 

$500,  due  in  3  yrs.,  and  bearing  interest  at  6%?  Ans.: 
P.  W.,  $475.81 ;  dis.,  $114.19. 

29.  Find  the  true  discount  at  6%  of  a  note  of  $300,  due  in  2 

yrs.,  and  bearing  8%  interest.    Ans.:  $37.29. 

30.  Find  the  present  worth  and  discount  of  a  note  of  $368.75 

for  5  mos.,  at  10%.    Ans.:  $354;  $14.75. 

31.  I  bought  goods  amounting  to  $775,  on  4  mos.  credit.    What 

would  I  pay  cash  if  money  is  worth  10%  ?    Ans.  :  $750. 

32.  If  money  is  worth  6%,  what  sum  in  cash  will  pay  for  a 

bill  of  goods  amounting  to  $260,  bought  on  8  months' 
credit  ?     Ans.  :  $250. 

33.  I  can  have  4  mos.  credit  or  5%  off  for  cash.     What  will  be 

my  gain  by  paying  cash  on  a  bill  of  goods  amounting 
to  $2,480,  if  money  is  worth  10  fc  ?    Ans.  :  $45.47. 

34.  The  difference  between  the  true  and  bank  discount  of  a 

certain  principal  is  $2.45  for  i  year.  What  is  the  princi- 
pal, int.  7%  (omitting  days  of  grace)?    Ans.:  $535. 

35.  I  was  oflfered  $r,i22  for  my  farm  in  cash,  or  $1,221  payable 

in  ID  mos.,  without  interest ;  I  chose  the  latter.  How 
much  did  I  lose,  money  being  worth  12%?    Ans.  :  $12. 

36.  I  bought  goods  on  9  mos.  credit,  amounting  to  $840.40. 
How  much  money  will  pay  the  debt  at  the  time  of  re- 
ceiving the  goods,  int.  being  8%?    Ans.:  $792,83. 

37.  A  30-day  note  yields  $1,650,  when   discounted  at  ij%  a 

month.     Find  the  face.     Ans.  :  $1,677.68. 

38.  A  note  discounted  at  8%  for  40  days  yields  $2,072.60.    Find 

the  face.    Ans.  :  $2,092.60 — . 

39.  At  what  should  I  discount  a  60  day  note  to  get  interest  at 

the  rate  of  20%?    Ans.:  19/07%- 

40.  What  is  the  rate  of  discount  when  a  note  running  i  yr. 

will  produce  25%  interest  without  grace  ?    Ans.  :  20^. 

41.  I  offered  to  sell  my  farm  for  $8,000  cash,  or  for  $10,296  in 

three  equal  payments,  at  the  end  of  i,  2  and  3  yrs.,  with- 
out interest.  If  money  is  worth  10^,  what  will  be  the 
gain  to  the  buyer  by  Dayiug  cash  ?    Ans.  :  $620* 


38  EXCHANGE. 


42.  What  will  be  the  face  of  my  note  if  I  wish  to  obtain  $400 

from  a  bank  for  30  days  when  discounted  at  6%?    Ans.  : 

$402.21. 

43.  The  bank  discount  on  a  certain  principal  for  i  yr.  at  6% 

is  $3  60  greater  than  the  true  discount  for  the  same  time 
and  rate.  Omit  days  of  grace  and  find  the  principal. 
Ans.:  $1,060. 


EXCHANGE. 


1.  What  is  the  cost  of  a  draft  on  Augusta  for  $5,680,  payable 

in  sixty  days,  exchange   being  2X  \%  prem.,  int.  6^? 
Ans.:  $5,648.76. 

2.  What  is  the  cost  of  a  draft  on  Albany  for  $1,575,  payable 

in  30  days,  exchange  being  at  f  %  premium,  int.  6%? 
Ans.:  $1,578.15- 

3.  The  face. of  a  draft  payable  in  60  days  is  $2,625,  exchange 

being  at  \\Jo  premium,  int.  6%.    Find  the  cost.    Ans.: 
$2,636.81+. 

4.  Find  the  cost  of  a  draft  for  $500,  payable  in  30  days  after 

sight,   exchange  being   1%  premium,  int.   dfo.    Ans.: 
$502.25. 

5.  How  large  a  draft  payable  30  days    after   sight  can  be 

bought   for  $502.25,  exchange  being  1%  premium  and 
int.  6%?    Ans.:  $500. 

6.  How  large  a  draft  payable  in  60  days  can  be  bought  for 

$798.80,  exchange  being  \\%  premium  and  interest  8%? 
Ans.:  $800. 

7.  A  draft   payable  in  30  days  was  bought  for  $352.62,  ex- 

change being  \\%  discount,  and  int.  6%.    Find  the  face. 
Ans.:  $360. 

8.  What  must  be  paid  in  Baltimore  for  a  draft  on  Cincinnati, 

drawn  at  90  days  for  $4,8  jo,  the  course  of  exchange  be- 
ing loif,  int.  6%?    Ans.:  $4,791.60. 


EXCHANGE.  39 


9.  A  commission  msrchant  in  Albany  wishes  to  remit  to  his 
employee,  in  Columbus,  by  draft  at  60  days,  $512.36. 
What  is  the  face  of  the  draft  he  can  purchase  with  this 
sum,  exchange  i^'fo  discount?    Ans.  :  $531.2184-. 

10.  What  must  be  paid  in  New  York  for  a  draft  on  Concord, 

at  30  days  for  $5,400,  exchange  \  %  premium  ?  Ans.  : 
$5,397-3o- 

11.  An  agent  in  Harrisburg,  Pa.,  having  $1,324.74  due  his  em- 

ployee, is  instructed  to  remit  the  same  by  a  draft  drawn 
at  30  days.  What  will  be  the  face  of  the  draft,  ex- 
change being  at  i|^  premium .?    Ans.  :  $1,309.03. 

12.  Exchange  on  Augusta,  Me.,  for  $5,000,  cost  $5,075.    What 

was  the  course  of  exchange  ?    Ans.  :  1^%  premium. 

13.  What  is  the  market  price  of  a  sight  draft  on  New  York 

for  $890,  exchange  being  ioiJ%?    Ans.  :  $901. 12J. 

14.  Find  the  market  value  of  a  sight  draft  on  New  York  for 

$1,800,  exchange  99%.     Ans.:  $1,782. 

15.  Find  the  cost  of  a  draft  on   Cincinnati  for  $1,400,  payable 

in  60  days  after  sight,  exchange  being  worth  io2j%,  and 
int.  being  7%.    Ans.:  $1,420.18^. 

16.  What  is  the  cost  of  a  draft  on  Peoria,  111.,  for  $2,400,  paya- 

ble in  90  days,  int.  being  10%,  and  exchange  103%? 
Ans.  :  $2,410. 

17.  Find  the  value  of  a  draft  on  Boston  for  $1,650,  payable  60 

days  after  sight,  exchange  being  98J,  and  int.  6% .  Ans.  : 
$1,607,925. 

18.  If  exchange  is   ioiJ%,  how  large  a   sight  draft  can  be 

bought  for  $7,900  ?    Ans.  :  $7,783.25. 

19.  What  is  the  face  of  a  draft  that  can  be  bought  for  $5,000, 

when  exchange  is  98^  ?    Ans.:  $5,076.14. 

20.  What  is  the  face  of  a  draft  at  60  days  sight,  which  costs 

$r,ooo,  exchange  being   103^   and  interest  6%?    Ans.: 

$980.87. 

21.  What  is  the  cost  of  a  si^ht  bill  for  ^87,  when  £1  is  wortl]^ 

$4.82  in  gold,  gold  being  worth  106  ?    Ans.  :  $444.5o-f . 

22.  How  large  a  bill  can  be  bought  for  $2,000  in  currency, 

when  sterling  exchange  is  quoted  at  $4.85  and  §old  at 
jp6?    Ans.:  ^389  7+d, 


40  EXCHANGE. 


23.  What  will  a  check  on  New  York  for  $1,505.40  cost  2X\^c 

discount?    Ans.:  $1,501.64—. 

24.  What  will  a  60-day  draft  on  Columbus  for  $12,692.50  cost 

at  f  %  premium,  int.  off  atSfc?    Ans.  :  $12,654.42-}-. 

25.  Find  the  face  of  a  draft  on  New  York  that  will  cost  $2,000 

at  1^  premium.     Ans.  :  $1,987.58—. 

26.  A  draft  cost  $4,681.25,  at  il%  discount.     Find  the  face. 

Ans.:  $4,740-51— • 

27.  What  must  be  the  face  of  an  18-day  draft  costing  $5,264.15 

at  ^^  premium,  int.  off  at  6%?    Ans.:  $5,256.27 — . 

28.  A  21-day  draft  cost  me  $6,836.75,  at  f  %  discount  and  in- 

terest off  at  6^.    Find  the  face.    Ans.  :  $6,925.04.  . 

29.  What  is  the  cost  of  a  60-day  draft  for  $850  on  New  York, 

exchange  being  at   loij,  int.  6fo  per  annum?     Ans.: 
$853-825. 

30.  The  cost  of  a  30-day  draft  was  $2,128,525,  exchange  being 

102,  int.  yfo.    Find  the  face.     Ans.:  $2,100. 

31.  What  is  the  cost  of  a  draft  of  $500  for  60  days  at  f  % 

premium,  int.  6%?    Ans.:  $498.50. 

32.  I  paid  $343.22  for  a  90-day  draft  at  ^%  discount,  and  int. 

6%.    Find  the  face.    Ans.:  $350,404-. 

33.  When  exchange  on  New  York  is  98^,  what  is  the  cost  of 

a  draft  for  $362  for  30  days,  int.  at  6%?    Ans.  :  $354.58—. 

34.  What  is  the  face  of  a  draft  payable  60  days  after  sight 

that  will  cost  $652,925,  exchange  ij%,int.  6%?    Ans.: 

$650. 

35.  The  face  of  a  draft  for  30  days,  exchange  being  98I,  and 

interest  6%,  was  $1,588,595.    Find  the  cost.    Ans.  :  $1,560. 

36.  What  will  be  the  cost  in  Nashville  of  a  sight  draft  on  Col- 

umbus for  $1,000,  the  rate  of  exchange  being  ^%  pre- 
mium?   Ans.:  $1,005. 

37.  If  exchange  on  Chicago  is  i\%  premium,  what  will  be  the 

cost  in   Memphis,  Tenn.,   of  a  sight  draft  of  $3,000? 
Ans.:  $3,037.50. 

38.  A  merchant  in   Chicago  bought  a  draft  on  Albany,  New 

York,  for  $5,000,  payable  30  days  after  sight.     Find  the 
cost  if  exchange  was  1%  premium.    Ans.  ;  $4,978.75. 


EXCHANGE. 

39.  What  will  be  the  cost  in  Lansing,  Mich.,  of  a  draft  for 

$1,500  on  Cleveland,  O.,  payable  90  days  after  date,  when 
exchange  is  ^  %  discount  ?    Ans.  :  $1,471,875. 

40.  How  much  will  be  realized  from  the  sale  of  a  draft  for 

$6,000  2X\fo  discount  ?    Ans.  :  $5,985. 

41.  How  much  will  be  realized  from  the  sale  of  a  draft  on 

Cincinnati  for  $3,000,  sold  at  \%  premium?  Ans.: 
$3>oo3-75. 

42.  When  exchange  is  looj,  what  will  be  the  cost  of  a  draft 

for  $5,000,  purchased  in  St.  Louis  on  Denver,  to  be  paid 
3  nios.  after  date  .?    Ans.  :  $4,928.75. 

43.  If  exchange  is  100^,  what  will  a  draft  for  $1,500  cost,  pur- 

chased in  Detroit,  Mich.,  on  Columbus,  payable  in  2 
mos.  without  grace  ?    Ans.  :  $1,488.75. 

44.  If  exchange  is  \%  premium,  what  will  a  draft  for  $1,500 

cost,  purchased  in  St.  Paul,  Minn.,  on  Zanesville,  O., 
payable  in  4  mos.  without  grace  .-*    Ans.  :  $1,473.75. 

45.  If  exchange  is   at  yV%  premium,  what  will  a  draft    br 

$5,000  on  Memphis,  Tenn.,  cost  in  New  York,  payable 
2  mos.  after  date  ?    Ans.  :  $4,952.50. 

46.  How  large  a  draft  on  N.  Y.  can  be  purchased  for  $5,000 

when  exchange  is  at  i\%  premium?    Ans.:  $4,926.11 — . 

47.  What  will  be  the  cost  of  a  sight  draft  on  N.  Y.  for  $5,725, 

when  exchange  is  |^%  premium?    Ans. :  $5,710.71-4-. 

48.  Find  the  face  of  a  30-day  draft  purchased  for  $1,500,  if  the 

rate  of  exchange  is  ^%  premium.    Ans.  :  $1,506.40. 

49.  If  I  pay  $1,200  for  a  draft  payable  in  2  mos.  when  the 

premium  on  exchange  is  ^%  and  the  rate  of  interest  is 
9% ,  what  is  the  face  of  the  draft  ?    Ans.  :  $1,213.04+. 

50.  How  large  a  sight  draft  on  St.  Paul  can  be  purchased  in 

N.  Y.  for  $10,000  if  exchange  \%  \%  discount?  Ans.: 
$10,012.51+. 

51.  How  large  a  draft  can  I  buy  on  Cincinnati  for  $1,750  if 

exchange  is  at  ^%  premium  ?    Ans.  :  $1,747.81+. 

52.  A  commission   merchant    in    Denver,   Col.,   sold    goods 

amounting  to  $3,500  for  a  man  in  N.  Y.  He  sent  the 
amount  due  by  a  draft  payable  in  30  da.  after  sight,  ex- 
change being  |  %  premium.  How  large  a  draft  did  he 
purchase  ?    Ans.  :  $3,5i4-93+' 


42  INSURANCE. 


53.  Find  the  face  of  a  draft  ou  I/ondon  that  can  be  bought  in 

N.  Y.  for  $3,762.50  in  currency  when  gold  is  at  105J  and 
exchange  is  at  I4.87.     Ans.  :  ^732  6s.  2.44-d. 

54.  When  exchange  is  $4.86  for  a  pound  sterling  and  gold  is 

at  107^,  what  will  be  the  face  of  a  draft  that  can  be 
bought  in  N.  Y.  on  London  for  $2,984.38?  Ans.:  /571 
4s.  6.64-d. 

55.  I  wish  to  obtain  a  bill  of  exchange  on  Paris,  at  sight  for 

3,269  francs.  What  will  it  cost,  exchange  being  at  5.15 
francs  to  the  dollar  and  gold  at  losf  ?    Ans.:  $668.87+. 

56.  When  exchange  is  at  5.19  francs  to  the  dollar  and  gold  at 

106^,  what  must  be  paid  in  currency  for  a  sight  bill  of 
exchange  on  Paris  for  8,950  francs?     Ans.:  $1,832.25 — . 

57.  Find  the  currency  value  of  a  draft  on  London  for  ;^895 

los.,  when  exchange  is  $4.87  for  a  pound  sterling  and 
gold  is  at  io6|.    Ans.  :  $4,65o+. 

58.  When  exchange  is  5.20  francs  for  a  dollar  and  gold  is 

worth  106^,  what  must  I  pay  for  a  sight  draft  on  Paris 
for  5,725  francs?    Ans.:  $1,169,774-. 

59.  I  purchased  a  sight  draft  on  London  for  ^585  los.  5d.    Find 

the  currency  value  of  the  draft,  if  exchange  was  at  par 
and  gold  107J.     Ans.  :  $3,059.05-!-. 

60.  Gold  is  quoted  at  104J.     Exchange  is  $4.88^.     Find  the 

cost  in  currency  of  a  sight  draft  on  London  for  ;i^875 
5s.  4d.    Ans.  :  $4,484.  II -|- 


INSURANCE. 


1.  I  insured  |  of  a  shop  worth  $3,600  and  f  of  a  store  worth 

$6,000.     Find  the  rate  of  insurance  if  I  paid  $126,  pay- 
ing $1  for  the  policy.     Ans.  :  \\fo. 

2.  It  cost  me  $75  for  insuring  a  store  for  f  of  its  value  at 

ii%.     What  was  the  store  worth  ?    Ans.  :  $10,000, 


INSUJ^ANCE.  43 


3.  Find  the  cost  of  insuring  f  <^f  ^  factory  at  f  %^  which  is 

valued  at  $340,000.     Ans.  :  1 1,328.124-. 

4.  I  paid  $17.25  for  insuring  f  of  a  building  at  i\'fo  ;  find  the 

value  of  the  house.     Ans.  :  $2,300. 

5.  I  paid  $39  for  insuring  a  building  worth  $4,550  at  i\%\ 

what  fraction  of  the  value  was  insured  ?    Ans.  :  f . 

6.  Find  the  cost  of  insuring  |  of  a  building  worth  $24,000 

and  f  of  another  worth  $36,000,  the  former  at  2^%,  the 
latter  at  ij%.     Ans.  :  $607.50. 


7.  A  shipment  of  goods  costing  $1,275  is  insured  at  f  ^,  the 

policy  costing  $1.00 ;  find  the  cost  of  insurance.     Ans.  : 

$8.08^. 

8.  I  paid  $19.20  for  insuring  f  of  a  barn  worth  $4,800.     What 

was  the  rate  ?    Ans.  :  f  ^. 

9.  I  insured  a  house  at  i\%\  reinsured  |  of  it  at  2%,  and  \ 

of  it  at  2\%\  what  rate  of  insurance  do  I  get  on  the 
remainder?    Ans.:  t\%. 

10.  I  took  a  risk  of  $45,000  ;  reinsured  at  the  same  rate  $1,000 

each  in  five  offices,  and  $5,000  in  another.  Find  the  rate 
of  insurance,  my  share  being  $262.50.     Ans.:  2|%. 

11.  I  took  out  a  life  policy  at  the  age  of  21  for  $5,000.     The 

annual  premium  is  $19.89  on  $1,000.  What  will  it  cost 
me  to  keep  up  my  insurance  if  I  live  to  be  75  yrs.  old? 
Ans.  :  $5,370.30. 

12.  I  wish  to  secure  an  endowment  policy  for  $1,000  payable 

in  10  yrs.,  annual  premium  costs  $104.58.  Find  the 
amount  of  the  10  payments,  allowing  int.  at  6%.  Ans.: 
$1,390.91+. 

13.  I  received  $118  for  insuring  a  building  at  |%.     Find  the 

value  of  the  building.     Ans.  :  $14,750. 

14.  I  received  $42.30  for  insuring  |  of  a  house  at  t*^%l  what  is 

the  value  of  the  house  ?    Ans.  :  $7,520. 

15.  My  share  of  the  premium  was  $197.13  after  taking  ^  of  a 

risk  at  2j%,  and  reinsuring!  of  it  at  2^%.  Find  the 
amount  of  the  risk.    Ans.  :  $262,840. 

16.  Took  a  risk  at  if,  reinsured  I  of  it  at  the  same  rate,  and 

I  of  it  at  ij%.  How  large  was  the  risk,  my  share  of  the 
premium  being  $58. 1 1  ?    Ans.  :  $19,370. 


44  INSURANCE. 


17.  I  insured  property  at  2^;  reinsured  $8,ocxd  at  i|%,  and 

$10,000  of  it  at  2\%.  What  was  the  amount  insured, 
my  share  of  the  premium  being  $207.50  ?    Ans.  :  $28,000. 

18.  For  how  much  must  a  ship  worth  $2,000  be  insured,  so 

that  the  insurance  will  cover  \  of  the  value  and  premium 
at  \\%}    Ans.:  $1,522,842. 

19.  I  received  $225  for  insuring  a  store  and  contents  for  |  of 

their  value  at  \\%.  The  stock  was  worth  \  as  much  as 
the  store.  Find  the  value  of  each.  Ans.  :  Stock, 
$6,666.661 ;  store,  $i3,333-33i. 

20.  I  paid  $325  for  insuring  my  store  for  $16,250.     What  was 

the  rate  of  premium  ?    Ans.  '.2%. 

21.  I  paid  $2,475  for  insuring  f  of  my  property  at  \\%.     Find 

the  amount  of  my  property.    Ans.  :  $297,000. 

22.  I  insured  my  property  for  f  of  its  value  at  2 J %,  paying 

$1,657.50.  What  was  the  value  of  my  property  ?  Ans.: 
$88,400. 

23.  I  paid  $400  for  having  |  of  my  property  insured  at  4^%. 

Find  the  value  of  the  property.    Ans.  :  $13,333.33^. 

24.  My  stock  of  goods  is  worth  $30,000 ;  insured  it  for  |  of  its 

value  at  f  %.  In  a  fire  I  saved  $5,000  of  goods.  What 
was  my  loss?    Ans.:  $25,168.75. 

25.  I  paid $180  for  insuring  my  stock  for  §  of  its  value  at  3%. 

What  is  the  value  of  the  stock  ?    Ans.  :  $9,000. 

26.  Mr.  Jones  paid  $652.50  for  insuring  a  mill  worth  $43,500. 

Find  the  rate.     Ans.:  i^^. 

27.  I  paid  $175  for  insuring  my  house  at  ij%.     It  was  de- 

stroyed by  fire.  How  much  insurance  did  I  procure  ? 
Ans.  :  $14,000. 

28.  What  will  be  the   annual   premium   on  a  life  policy  of 

$5,000  at  $21  10  per  $r,ooo?    Ans.:  $105.50. 

29.  A  person  33  years  of  age  pays  $123,90  annual  premium  on 

a  life  insurance  policy  of  $5,000.     Find  the  rate.    Ans.: 

30.  My  building  is  worth  $150,000  and  is  insured  for  \  of  its 

value  in  three  companies ;  the  first  takes  a  \  risk  at  |%, 
the  2d  a  ^  risk  at  f  %,  and  the  3d  the  remainder  at  f  ^. 
What  is  the  premium?    Ans.  :  $717.18. 


TAXES.  45 


My  ^oods  worth  $6,000,  and  insured  at  2,J%,  were  damaged 
654%.  What  did  the  company  have  to  pay  above  the 
premium  ?    Ans.  :  $3,810. 

32.  I  bought  1,500  bu.  of  wheat  at  $1.10  per  bushel,  and  had  it 

insured  at  $1.20  per  bushel  at  2^%.  It  was  all  destroyed 
by  fire  ;  what  is  my  gain  ?    Ans.  :  $105. 

33.  An  insurance  company  took  a  risk  on  a  vessel  for  $100,000 

at  1%,  but  deeming  the  risk  too  great  reinsured  $60,000 
at  Ifc'y  what  was  the  amount  received  more  than  paid? 
Ans.  :  $225. 

34.  The  premium  at  3%  is  $378 ;  what  is  the  value  of  the  prop- 

erty insured?    Ans.  :  $12,600. 

35.  At  what  must  property  worth  $1,950  be  insured  at  2j%  so 

as  to  include  premium  in  case  of  loss  ?    Ans.  :  $2,000. 

36.  I  had  9,700  bushels  of  wheat  worth  $1.20  per  bushel ;  I  had 

it  insured  at  3%,  so  as  to  cover  premium  and  loss.  For 
what  was  it  insured  ?    Ans.  :  $12,000. 

37.  For  what  sum  must  I  have  my  property  worth  $2,600  in- 

sured, premium  at  xV%>  to  cover  property?  Ans.: 
$2,618.26+. 


TAXES. 


Find  the  tax  to  be  raised  in  a  township  whose  taxable 
property  is  worth  $486,250,  the  rate  of  taxation  being  78 
cts.  on  $100.    Ans.  :  $3,792.75. 

My  property  is  assessed  at  $3,800.  What  is  my  whole  tax 
if  the  rate  of  taxation  is  xV(J%  ^^^  ^  V^Y  ^  poll-tax  of 
$1  ?    Ans.  :  $30.64. 

My  whole  tax  is  $53.46.  I  pay  for  3  polls  at  $1.50  each.  I 
own  $8,704  taxable  property.  Find  the  rate  of  taxation. 
Ans.  :  56^  cts.  on  $100. 

My  income  is  16%  of  my  capita.  I  am  taxed  2}%  of  my 
income  and  pay  $26.04.  Wlhat  is  my  capital  ?  Ans.  : 
$6,510. 


46  DUTIES  OR  CUSTOMS. 


5.  I  sold  my  property  for  $7,599,  whic'i  was  cost,  and  1%  be- 

sides paid  for  tax.     What  was  the  cost  ?    Ans.  :  $7,450. 

6.  I  pay  a  tax  of  $1.35  on  $100  on  my  capital  and  I  have  left 

$125,127.66.  What  was  my  capital  and  tax  ?  Ans.:  Capi- 
tal, $126,840 ;  tax,  $1,712.34. 

7.  Find  the  value  of  the  taxable  property  in  a  village  con- 

taining 1,024  polls  paying  $1  each,  that  pays  a  tax  of 
$4,000,  taxation  being  2.4  mills  on  the  dollar.  Ans.  : 
$1,240,000. 

8.  A's  real  estate  is  assessed  at  $4,300,  and  personal  property 

at  $1,940;  pays  for  2  polls  at  $1 ;  is  taxed  $33.20.  What 
was  the  %  of  tax?    Ans.:  Y/c. 

9.  In  a  township  whose  valuation  is  $6,748,950,  the  rate  of  tax 

is  3xV%I  the  collector  is  paid  \\%  for  collecting.  What 
is  the  amount  collected,  and  what  are  the  collector's 
fees?    Ans.:  Amount,  $239,317.76;  fees,  $3,644.43+. 


DUTIES  OR  CUSTOMS. 


1.  Find  the  duty  on  3  boxes  of  tin  weighing  11 1,  112  and 

113  lbs.,  respectively,   at  5  cts.   a  lb.,    tare  5^.     Ans.: 
$15.96. 

2.  What  is  the  duty  at  4%  on  20  boxes,  each  containing  250 

lbs.  of  tobacco  costing  20  cts.  a  lb.,  tare  (i\%'>    Ans.: 
$37-50. 

3.  I  received  3,724  yds.  of  cloth  invoiced  at  23  cts.  a  yd. ;  the 

duty  is  10  cts.  a  yd.  and  1 1  %  ad  valorem,  less  10% .    What 
is  the  total  amount  of  duty?    Ans.  :  $419  96  — . 

4.  Find  the  duty  on  45  barrels  of  whisky,  each  containing  36 

gal.,  invoiced  at  $1.25  per  gal.,  at  40%  ad  valorem,  al- 
lowing 2%  for  leakage.     Ans.:  $793.80. 

5.  What  is  the  duty  on  12  98-lb.  boxes  of  soap,  tare  10%,  at  5 

cts.  a  lb.  ?    Ans.  :  $52.92. 


DUTIES  OR  CUSTOMS.  47 

6.  What  is  the  duty  on  36  boxes  of  sugar,  each  weighing  668 

lbs.,  at  2j  cts.  a  lb.,  deducting  \  of  the  entire  weight  for 
tare?    Ans.  :  IsiS-S^- 

7.  Find  the  duty  on  oilcloth  40  yds.  long  and  3I  yd.  wide, 

worth  75  cts.  a  sq.  yd.,  at  30%  ad  valorem.  Ans.: 
$35-07+. 

8.  What  is  the  duty  on  30  bags,  each  weighing  760  lbs.,  tare 

12% ,  at  $1.20  a  cwt. .?    Ans.  :  $240,764-. 

9.  What  is  the  cost  per  gal.  of  Jamaica  rum  if  I  pay  $631.43 

for  1,680  gal.,  duty  15%,  leakage  2%,  charges  $53.34? 
Ans.  :  30  cts.-f. 

10.  Find  the  invoice  price  of  an  amount  of  cloth  after  paying 

30%  duty  and  other  charges  $73.80,  and  cost  in  store 
$7,389-03-    Ans.  :  $5,627.10. 

11.  A  wine  merchant  imported  60  casks  of  wine,  54  gal.  each, 

invoiced  at  $1.80  a  gal.,  transportation  25  cents  a  gallon, 
charges  $8.50,  leakage  5%  and  duty  20^.  What  was  the 
entire  cost  ?    Ans.  :  $7,758.58. 

12.  I  paid  $184.80  duty  on  50  bbls.  of  sugar,  weighing  220  lbs. 

each,  gross  tare  4%,  invoiced  at  5  cts.  a  pound.  What 
was  the  rate  ?    Ans.  :  35%. 

13.  What  is  the  duty  at  15%  on   540  bags  of  coffee,   gross 

weight  160  lbs.  each,  tare  3^%,  invoiced  at  9  cts.  a  pound? 

Ans.:  $1,125.57+. 

14.  What  is  the  duty  at  28%  on  25  cases  of  cloth  containing 

24  pieces  each,  45  yds.  in  a  piece,  and  worth  $1.13  a  yard? 
Ans.:  $8,542.80. 

15.  What  is  the  duty  on  12  barrels  of  whisky  of  42  gal.  each, 

invoiced  at  $1.30  per  gallon  at  31 J %,  leakage  5%?  Ans.  : 
$196.07-. 

16.  A  imported  40  rolls  of  carpet,   160  yds.   each,   and   paid 

$1,024  tiuty  at  20%.  At  what  price  per  yd.  was  the  carpet 
invoiced  ?    Ans.  :  80  cts. 

17.  What  is  the  duty  on  20  boxes  of  raisins  of  25  lbs.  each, 

valued  at  10  cts.  a  pound,  allowing  15%  for  tare,  when 
the  rate  of  duty  is  6%  ad  valorem  ?    Ans.  :  $2.55. 

18.  What  is  the  duty  on  7  tons  of  steel  of  2,240  lbs.  each,  in- 

voiced at  17  cts.  per  lb.  when  the  rate  of  duty  is  20^  ad 
valorem?    Ans.:  $533.12, 


48  PROPORTION. 


19.  Find  the  duty  on  20  hhds.  molasses,  each  containing  63 

gal.,  at  9  cts.  per  gal.,  allowing  5%  for  leakage.  Ans.  : 
$107- 73- 

20.  What  is  the  duty  on   10  barrels  of  Havana  tobacco,  each 

weighing  145  lbs.  gross,  tare  8%,  at  6|  cts.  a  pound? 
Ans.:  $90.04-1-. 

21.  When  there  is  a  duty  on  tea  of  10  cts.  a  pound,  what  must 

be  paid  on  45  chests  of  tea,  each  weighing  120  lbs.,  tare 
10 %?    Ans.:  $486. 

22.  What  is  the  duty  on  210  bags  of  coffee,  the  gross  weight 

of  each  being  190  lbs.,  invoiced  at  5  cts.  a  pound,  the 
tare  being  5%  and  duty  25%?    Ans.  :  $473.81+. 

23.  What  is  the  duty  at  40%  ad  valorem  on  15  cases  of  broad- 

cloth, each  containing  25  pieces  of  35  yds.,  invoiced  at 
$3.95  a  yd.     Ans.  :  $20,737.50. 

24.  The  duty  on  15  gross  of  bottle  beer,  allowing  10%  break- 

age, was  $40.50  at  20%  ad  valorem.  How  much  a  dozen 
were  they  invoiced  at?    Ans.  :  $1.25. 

25.  The  duty  on  100  pieces  of  silk  of  18  yds.  each  was  $337.50 

at  25%  ad  valorem.  What  was  the  invoice  price  per  yd., 
and  what  must  I  sell  it  per  yd.  to  gain  20%?  Ans.  :  In- 
voiced at  75  cts.  per  yd. ;  selling  price  $i.i2j. 

26.  Paid  $806.12  duty  on  cloth  at  35%.    What  were  they  in- 

voiced at,  and  what  did  they  cost  in  store?  Ans.:  In- 
voiced at  $2,303.17 ;  cost  $3,109.27-1-. 

27.  I   pay  a  duty  of  $1,473.80  on  goods  valued  at  $3,684.50. 

What  is  the  rate  of  duty  ?    Ans.  :  40%. 


PROPORTION. 


1.  The  first,  third  and  fourth  terms  are  8.4,  9J  and  5J.    What  i 

is  the  second?    Ans.  :  4.95.  \ 

2.  The  last  three  terms  are  9^,  \\  and  8^.     What  is  the  first  j 

term?    Ans.:  i|.  1 


PROPORTION.  49 


3.  If  I  can  build  f  rods  of  wall  in  f  of  a  day,  how  much  can 

I  build  in  -^-^  of  a  day  ?    Ans.  :  x%  rd. 

4.  35  men  have  flour  for  24  days.     If  14  leave,  how  long  will 

it  feed  the  remainder  ?    Ans.  :  40  days. 

5.  If  the  consequent  is  f  and  the  ratio  \,  what  is  the  ante- 

cedent ?    Ans.  :  aV* 

6.  If  the  antecedent  is  6  and  the  ratio  i|,  what  is  the  conse- 

quent ?    Ans.  :  5. 

7.  What  is  the  ratio  of  a  pound  troy  to  a  pound  avoirdupois? 

Ans.:  ill. 

8.  What  is   the   difference  between   the   compound    ratios 

9.  What  is  the  difference  between  the  ratio  4f  :  7J  and  the 

inverse  ratio  ?    Ans.  :  \\\\. 

10.  If  the  ratio  is  2\  and  the  consequent  is  6J,  what  is  the 

antecedent  ?    Ans.  :  14^. 

11.  Find  the  inverse  ratio  of  the   two   numbers  ^\  and  2 J. 

Ans.:  f. 

12.  A  certain  number  has  been  divided  by  one  more  than  it- 

self, giving  a  quotient  \.     What  is  the  number?    Ans.  :  \. 

13.  If  48  lbs.  of  salt  water  contain  \\  lbs.  of  salt,  how  much 

fresh  water  must  be  added  to  these  48  lbs.  so  that  40  lbs. 
of  the  mixture  shall  contain  \  lb.  of  salt  ?    Ans.  :  72  lbs. 

14.  Divide  the  number  3I  into  two  such  parts  that  the  first 

shall  equal  the  second  plus  jV    Ans.  :  i|f  and  if  ^. 

15.  A,  B  and  C  earned  $3,456  ;  B  earned  3  times  as  much  as  C 

and  A  4  times  as  much  as  B.    How  much  did  each  earn  ? 
Ans.  :  A,  $2,592;  B,  $648;  C,  $216. 

16.  A  and  B  have  2,255  l>u.  of  corn  ;  |  of  A's  equals  \  B's 

amount.     How  many  bushels  has  each?    Ans.  :  A,  1,100; 
B,  1,155. 

17.  The  difference  between  two  numbers  is  120,  and  \  of  the 

first  equals  f  of  the  second.     What  are  the  numbers  ? 
Ans.  :  1,296  and  1,176. 

18.  The  sum  of  two  fractions  is  ly^.  and  |  of  the  first  equals 

f  of  the  gecoud,    Find  the  fractioi^s,    Ans.  :  \  and  |. 


50  PARTNERSHIP. 


19.  John  has  $637  less  than  James,  and  |  of  James'  equals  \\ 

times  John's.  How  much  has  each  ?  Ans.  :  John,  $728 ; 
James,  $1  365. 

20.  A  and  B  have  13,650  sheep ;  5  times  A's  equals  8  times  B's. 

How  many  has  each  ?    Ans.  :  A,  8,400 ;  B,  5,250. 

21.  A  bought  a  farm,  store  and  a  house  for  $28,100.     The  farm 

cost  three  times  as  much  as  the  house,  plus  $450  ;  and 
the  store  cost  twice  as  much  as  the  farm,  minus  $650. 
What  was  the  cost  of  each  ?  Ans.  :  Store,  $16,450;  farm, 
$8,550;  house,  $2,700. 


PARTNERSHIP. 


1.  A,  B  and  C  buy  property  for  $2,500;    A  pays  $500;   B, 

$1,200;  C,  $800;  they  rent  it  for  $300.  What  is  each 
one's  share  of  the  rent?  Ans.:  A's,  $60  ;  B's,  $144  ;  C's, 
$96. 

2.  X,  Y  and  Z  rent  a  farm  for  $1,200;  X  pastures  16  cows; 

Y,  14  cows,  and  Z,  12  cows.  How  much  should  each 
pay  ?    Ans.  :  X,  $457} ;  Y,  $400 ;  Z,  $342!-. 

3.  A,  B  and  C  buy  a  store ;  A  puts  in  $18,000 ;  B,  $6,000 ;  C, 

$10,000 ;  they  lose  30%  of  their  stock  by  fire  and  sell  the 
remainder  at  a  gain  of  50%.  What  is  each  one's  share 
of  the  gain  ?    Ans.  :  A's,  $900 ;  B's,  $300  ;  C's,  $500. 

4.  What  is  the  stock  of  each,  when  A,  B  and  C  gain  $2,250; 

A's  gain  is  $800,  B's  gain  is  $1,000,  and  C's  capital  is 
$3,000?    Ans.  :  A's,  $5,333^  \  B's,  $6,666f. 

5.  Ray  Jones  willed  his  son  $6,500;  his  wife,  $8,000,  and  his 

daughter,  $5,500 ;  his  estate  amounted  to  only  $12,000. 
What  did  each  get?  Ans.:  S,  $3,900;  W,  $4,800;  D, 
$3,300- 

6.  A,  B  and  C  buy  a  store  for  $16,000;  A  pays  $5,000;  B, 

$6,500;  C,  $4,500;  they  pay  $2,500  for  clerks,  $600  for 
rent,  then  sold  out  for  $23,000,  What  did  each  gain? 
Ans.:  A,  $1,218.75;  B,  $1,584  37*;  ^$1,096.87^. 


PARTNERSHIP.  5t 

7.  X,  Y  and  Z  hire  a  pasture  for  $87.20 ;  X  puts  in  3  cows  for 

16  weeks ;  Y,  5  cows  for  20  weeks ;  and  Z,  7  for  10  weeks. 
How  much  does  each  pay,  and  what  is  the  pasturage  of 
a  cow  per  week?  Ans.  :  X,  $19.20;  Y,  $40;  Z,  $28;  P, 
40  cts.  a  week. 

8.  A,  B  and  C,  on  closing  business,  paid  $2,706.    A  had  $4,200 

invested  ;  B,  $3,600  ;  C,  $4,500.  What  amount  did  each 
pay  ?    Ans.  :  A,  $924 ;  B,  $792  ;  C,  $990. 

9.  A,  B  and  C  do  a  piece  of  work  for  $1,600 ;  A  furnishes  7 

men  30  days ;  B,  5  men  40  days,  and  C,  6  men  32  days. 
How  much  should  each  receive  if  they  pay  $95  for 
clerks  ?    Ans.  :  A,  $525  ;  B,  $500 ;  C,  $480. 

10.  X  invested  $675  ;  B,  $810  for  the  same  time  ;  X's  gain  was 

$125.    What  was  the  whole  gain  ?    Ans.  :  $275. 

11.  A  invested  $2,500;  two  months  afterward  B  joined  him 

with  $3,000 ;  in  two  yrs.  they  cleared  $2,835.  Divide 
their  gain.    Ans.  :  A,  $1,350;  B,  $1,485. 

12.  A,  B  and  C  invested  $1,000  each  ;  A's  money  was  in   10 

mos. ;  B's,  12  mos. ;  C's,  14  mos. ;  they  sold  for  $2,730. 
What  did  each  lose .?    Ans.  :  A,  $75  ;  B,  $90  ;  C,  $105. 

13.  Divide  756  into  two  parts,  which  shall  be  to  each  other  as 

7.5  to  |.    Ans.  :  720  and  36. 

14.  Divide    10.25    into  two  parts  to  each  other  as  if  to   2J. 

Ans.:  4.1  and  6.15. 

15  A,  B  and  C  bought  a  horse  for  $100,  sold  at  a  gain  of  50%, 
by  which  A  gained  $18,  and  B  $19.  How  much  did  each 
pay  for  the  horse?    Ans.  :  A,  $36  ;  B,  $38 ;  C,  $26. 

16.  A  pastures  8  horses  3  weeks  2  days  ;  B,  12  horses  4  weeks 

I  day.     What  part  should  each  pay?     Ans.  :  A,  y^a  ;  B, 

17.  A  company  charter  a  boat  for  a  picnic  for  $50 ;  having  but 

210  to  go,  they  receive  on  board  another  company  of 
140.    What  should  the  second  company  pay  ?    Ans.  :  $20. 

18.  A  and  B  rent  a  lot  for  $50 ;  on  dividing,  A's  tract  is  80 

yds.  long  and  60  yds.  wide  ;  B's,  64  rds.  long  and  50  rds. 
wide.    What  should  each  pay  ?    Ans.  :  A,  $30  ;  B,  $20. 


52  EQUA  TION  OF  PA  YMENTS. 


19.  A,  B  and  C  gaiu  $3,250;  A  puts  in  $2,500;  B,  $1,500;  after 

9  mos.  they  take  in  C  with  $5,000;  9  mos.  after  this  they 
quit.  Divide  their  gaiu.  Ans.  :  A,  $1,250;  B,  $750;  C, 
$1,250. 

20.  X  and  Y  hire  a  pasture  for  $275  ;  X  puts  in  80  sheep  and 

Y  100 ;  after  6  mos.  they  each  sell  h  of  their  sheep,  and 
allow  C  to  feed  50  sheep  the  rest  of  the  yr.  How  much 
should  each  pay?  Ans.:  A,  $103.12^;  B,  $128.90!;  C, 
$42.96^. 

21.  A's  stock  is  to  B's  as  4  to  5  ;  after  3  mos.  A  withdraws  ^ 

of  his  and  B  ^  of  his.  Divide  $1,695  at  the  end  of  the 
year.     Ans.  :  A,  $720 ;  B,  $975. 

22.  A,  B  and  C's  capital  is  as  2,  ^,  J  ;  after  4  mos.  A  takes  out 

J  of  his;  after  9  mos.  more  their  gain  was  $1,988.  Di- 
vide it.     Ans.  :  A,  $714  ;  B,  $728  ;  C,  $546. 

23.  A's  capital  is  $4,200;  B's  $5,600;  after  4  months  how  much 

must  A  put  in  to  entitle  him  to  half  the  year's  gain  ? 
Ans.:  $2,100. 

24.  A  furnishes  404  bus.  of  corn  at  50  cts.  per  bu. ;  B,  340  bus. 

of  wheat  at  $1.10  per  bu.  ;  they  gain  $31.68.  What  did 
each  gaiu?     Ans.:  A,  $ii.ii;  B,  $20.57. 

25.  A  put  in  $7,000  for  6  mos. ;  B  put  in  $5,000  and  received  j^j- 

of  the  profit.  How  long  was  his  money  invested  ? 
Ans.  :  7  mos. 


EQUATION  OF  PAYMENTS. 


1.  I  wish  to  pay  $600  in  one  payment,  instead  of  paying  $50 

on  the  first  day  of  each  mo.  of  the  yr.     When  should  I 
pay  it  ?     Ans.  :  In  5f  mos. 

2.  I  owe  $900,  due  in   12  morths;  if  I  pay  $300  now,  when 

shall  I  pay  the  balance  ?     Ans.  :  18  mos. 

3.  Bought  goods  as  follows  :    Jan.  15,  $30 ;  Jan.  27,  $80 ;  Feb. 

8,  $70;  Feb.  24,  $60.     Find  the   equated   time.    Ans.; 
Feb.  5. 


TION  OF  PA  YMENTS.  53 


4.  May  I,  I  owe  $300 ;  July  12,  $700 ;  and  Sept.  22,  $Soo,    When 

may  I  pay  them  all  together?     Ans  :  Aug.  i. 

5.  I  exchanged  three  notes  :  one  of  $500  at  4  nios.,  $600  at  5 

mos.,  and  $400  at  7  mos,,  for  one  of  $1,500.  How  long 
should  the  ii,5oo  note  run .?     Ans.  :  5  mos.  6  days. 

6.  I  owe  $900,  due  Jan.  12;  $r,ooo,  July  12;  and  $r,ico,  Set  t. 

12.     When  can  I  pay  them  all  together?     Ans.  :  Junr  11. 

7.  A  owes  I500  due  May  4,  and  $500  May  26.     When  sli   u-d 

both  be  paid?     Ans.:  May  15. 

8.  Suppose  I300  is  due  in  14  days,  and  $6,000  in  35  days.     At 

what  time  should  both  be  paid  ?    Ans.  :  In  34  days. 

9.  1  bought  a  farm  for  $10,500,  payable  in  6  mos.  ;  I  paid 

$2,000  in  2  mos.,  and  $4,500  in  4  mos.  How  much  time 
should  I  have  on  the  remainder  ?     Ans  :  11^  mos. 

10.  Bought  a  house  for  $ro,ooo,  to  be  paid  for  as  follows :     \  in 

6  mos.,  I  in  I  yr.  6  mos.,  and  the  remainder  in  i\  yrs. 
Find  the  average  time  of  payment.  Ans.:  i  yr.  9  mos. 
18  days. 

11.  I  paid  $600  in  5  mos.,  $1,000  in  10  mos.,  $1,200  due  in  7f 

mos.  What  would  have  been  the  average  time  of  pay- 
ment?   Ans.:  8  mos. 

12.  I  sold  $2,100  worth  of  goods  Apr.  i,  to  be  paid  as  follows : 

$300  in  4  mos.,  $800  in  5  mos.,  and  $1,000  in  8  mos. 
Find  the  equated  time  of  payment.     Ans.  :  6f  mos. 

13.  I  bought  $1,800  worth  of  wheat  June  i,  to  be  paid  for  as 

follows  :  $300  in  30  days,  $600  in  60  days,  and  $900  in  90 
days.  What  is  the  equated  time  of  payment  ?  Ans.  : 
Aug.  10. 

14.  I  owe  $840  due  Oct.  3  ;  if  I  pay  $400  July  i,  $200  Aug.  i, 

when  should  I  pay  the  balance  ?  Ans.  :  Apr.  30,  next 
year. 

15.  I  bought  a  house  and  lot  for  $12,000,^  in  cash  and  the 

balance  in  two  equal  payments  at  3  and  6  mos. ;  I  pay 
\  down  and  the  balance  in  three  equal  payments  at 
equal  intervals.     What  is  the  interval  ?     Ans.  :  2  mos. 

16.  I  exchanged  three  notes,  $300  due  in  10  days,  $500  due  in 

25  days,  $1,000  due  in  40  days,  for  $600  cash  and  two 
notes  for  $550  and  $650  due  at  equal  intervals.  Find  the 
interval.     Ans.  :  30  days. 


54  ALLIGATION. 


17.  I  owe  a  certain  sum,  \  of  which  is  due  in  3  mos.,  ^  iu  6 

mos.,  and  the  remainder  in  8  mos.  What  is  the  average 
time  of  payment?    Ans.  :  5I  mos. 

18.  I  lent  A  $400  for  6  mos. ;  at  another  time  $600  for  8  mos. 

For  how  long  a  time  must  A  lend  me  $900  to  balance 
the  favor  ?     Ans.  :  8  mos. 

19.  A  owes  $600,  due  in  6  mos. ;  4  mos.  before  it  is  due  $200  is 

paid,  and  2  mos.  before  it  is  due  $200  more  is  paid.  How 
long  after  the  expiration  of  the  6  mos.  may  the  remain- 
ing $200  remain  unpaid  ?    Ans.  :  6  mos. 


ALLIGATION. 


1.  I  mix  3  lbs.  of  sugar  at  10  cts.,  5  lbs.  at  8  cts.,  and  2  lbs.  at 

15  cts.  What  is  the  average  price  per  pound?  Ans.: 
10  cts. 

2.  How  much  worsted  goods  at  10,  13  and  15  cts.  a  yard  must 

I  sell  that  the  average  price  may  be  12  cts.  a  yard? 
Ans.  :  4  at  10  cts.,  2  at  13  cts.,  and  2  at  15  cts. 

3.  A  buys  hogs  at  $5,  $6,  $7  and  $ro  a  head ;  how  many  of 

each  did  he  buy  if  the  average  price  was  $7.50  ?  Ans.  : 
I  at  $5,  5  at  $6,  5  at  $7  and  5  at  $10. 

4.  How  many  pounds  of  coflfee  at  12,  15,   18  and  20  cts.  a 

pound  must  be  sold  that  the  average  price  per  pound 
may  be  16  cts.?  Ans.  :  i  at  12,  2  at  15,  i  at  18  and  i  at 
20  cts. 

5.  A  merchant  sold  25  yards  of  ribbon  at  12  cts.  a  yard  ;  how 

much  must  he  sell  at  8  and  15  cts.,  respectively,  that 
the  average  price  maybe  13  cts.?  Ans.:  25  yds.  at  8 
cts.,  25  at  12,  and  75  at  15  cts. 

6.  I  buy  corn  at  60,  62  and  65  cts.  a  bushel ;  how  much  did  I 

buy  of  each  if  I  bought  70  bu.  at  70  cts.  a  bu.,  and  the 
average  price  is  67  cts.  ?    Ans.  :  1$  bu.  of  each, 


ALLIGATION,  55 


7.  I  have  6  gal,  of  rum  95%  strong  and  some  90%  strong; 

how  much  water  and  how  much  of  the  90%  rum  must 
be  mixed  with  the  6  gal.  that  the  strength  may  be  re- 
duced to  80%?    Ans.  :  3  gal.  at  90%,  and  i^  gal.  water. 

8.  How  much  sugar  at  8,  9,  12  and  15  cts.  a  pound  must  be 

mixed  so  as  to  fill  an  order  of  300  lbs.  at  10  cts.  ?  Ans.  : 
150  at  8  cts.,  60  at  9  cts.,  30  at  12  cts.,  and  60  at  15  cts. 

9.  B  hired  10  laborers  for  5  weeks,  consisting  of  men  and 

boys,  men  at  $15  a  week,  and  boys  at  $5  a  week  ;  he  paid 
them  all  $450 ;  how  many  were  there  of  each  ?  Ans.  :  4 
men  and  6  boys. 

10.  Sold  100  lbs.  of  coffee  for  $33  ;  some  sold  at  30  cts.,  some 

at  28  cts.,  and  some  at  35  cts.  a  pound;  how  many 
pounds  were  there  of  each?  Ans.:  12  at  30  cts.,  20  at 
28  cts.,  and  68  at  35  cts. 

11.  I  buy  geese  at  85  cts.,  ducks  at  30  cts.,  and  chickens  at  40 

cts.  each;  in  all,  80  fowls  for  $48;  how  many  of  each 
were  there  ?    Ans.  :  40  geese,  20  ducks  and  20  chickens. 

12.  What  is  the  average  price  of  7  articles,  5  at  $1  each,  the 

others  at  2  cts.  each  ?    Ans.  :  72  cts.  each. 

13.  A  man  mixed  4  gal.  of  whisky  at  50  cts.  a  gal.,  2  quarts  of 
V  alcohol  at  80  cts.  a  qt.,  and  i  gal.  of  water ;  what  was 

the  mixture  worth  per  gal.  ?    Ans.  :  50rx  cts. 

14.  What  relative   number  of  sheep  at  $3,  $5  and  $10  a  head 

can  be  bought  at  an  average  value  of  $7  per  head  ?  Ans.  : 
I  at  $3,  I  at  I5  and  2  at  $10. 

15.  I  have  a  compound  containing  15  lbs.  of  copper,  whose 

specific  gravity  is  7I;  \  lb.  of  silver,  specific  gravity 
\o\\  and  8  lbs.  of  iron,  specific  gravity  6|.  What  is  the 
specific  gravity  of  the  compound  ?    Ans.  :  72^0  i»early. 


s6  ARITHMETICAL  PROGRESSION. 


ARITHMETICAL  PROGRESSION. 


1.  The  first  payment  was  50  cts,,  the  2d  53,  the  3rd  56,  and  so 

on.    What  was  the  19th  payment  ?    Ans.  :  $1.04. 

2.  Find  the  20th  term  of  a  decreasing  series  whose  first  term 

is  94,  second  92,  and  so  on.    Ans.  :  56. 

3.  First  term  43,  com.  dif.  y\  ;  find  the  37th  term  of  an  in- 

creasing series.     Ans.  :  64. 

4.  If  A  makes  $939  the  first  month,  and   each  succeeding 

month  $80  less,  find  the  profits  in  one  year.    Ans.  :  $5,988. 

5.  If  100  apples  were  placed  two  yds.  apart  in  a  straight  line, 

what  distance  must  a  person  travel  to  gather  them 
singly  into  a  basket  placed  in  line  and  2  yds.  from  the 
first  apple  ?     Ans.  :  i\\\  mi. 

6.  I  sold  1,000  sheep  at  10  cts.  for  the  first,  20  for  the  second, 

and  30  for  the  third,  etc.  What  did  I  receive  for  the 
sheep?    Ans.:  $50,050. 

7.  I  employed  a  clerk  on  the  following  terms  for  10  mos. : 

$20  for  the  first  mo.;  $30  for  the  second,  $40  for  the 
third,  etc.  What  did  I  pay  for  the  whole  time  ?  Ans.  : 
$650. 

8.  A  board  10  ft.  long  is  2J  in.  wide  at  the  narrow  end  and 

increases  in  width  i^  in.  for  every  foot  in  length.  What 
is  the  width  of  the  wide  end?    Ans  :  16  inches. 

9.  The  first  term  is  4,  the  last  term  49,  the  number  of  terms 

10.    What  is  the  sum  of  the  series  ?     Ans.  :  265. 

10.  A  buys  a  farm  on  monthly  payments,  to  be  paid  in  3  yrs. 
10  mos.  The  5th  payment  was  $21.  the  20th  $60.  What 
did  he  pay  for  the  farm  ?    Ans.  :  $2,971.60. 


GEOMETRICAL  PROGRESSION.  57 


GEOMETRICAIv  PROGRESSION. 


I.  A  travels  96  mi.  the  first  day,  and  on  each  succeeding  day 
\  as  far  as  on  the  preceding  day ;  how  far  did  he  go  on 
the  5th  day  ?    Ans.  :  30  mi.  3  fur. 

(2.  What  is  the  7th  term  of  the  series  128,   192,  288,  etc.? 
f         Ans.  :  1458. 
•3.   A  hound  and  a  fox  are  20  rds.  apart.     The  hound  runs  10 
rds.  while  the  fox  runs  9  rds.     At  this  rate  how  far  will 
the  hound  run  to  catch  the  fox  ?     Ans.  :  200  rds. 

4.  B  engaged  to  work  20  da.  for  ^  of  a  cent  for  the  first  day, 

I  cent  for  the  second,  2  cents  for  the  third,  and  so  on. 
How  much,  at  this  rate,  will  he  receive  for  the  20  days  ? 
Ans.:  $5,242.87 J. 

5.  What  is  the  last  term  in  the  series  whose  3d  term  is  16 ; 

and  common  ratio  6 ;  number  of  terms  9  ?    Ans.  :  746,496. 

6.  Suppose  the  33d  term  is  1,024,  common  ratio  \  ;  find  the 

40th  term.    Ans.  :  136^^. 

7.  Find  the  sum  of  the  infinite  geometrical  series  of  i,  J,  t, 

etc.    Ans.  :  2. 

8.  Find  the  sum  of  the  infinite  geometrical  series  of  i|,  i,  f, 

etc.    Ans.  :  8^. 

9.  The  first  term  is  8  ;  fourth  term  512.     Find  the  common 

ratio.     Ans.  :  4. 

ID.   Insert  one  geometric  mean  between  3  and  27.     Ans.  :  9. 

II.  Insert  two  geometric  means  between  4  and  32.    Ans.:  S 
and  16. 


5^  TIME. 


TIME. 


1.  The  time  past  noon  is  I  of  the  time  past  midnight.    What 
is  the  hour  ?    Ans.  :  8  o'clock  p.  m. 

1.  The  time  past  noon  is  \  of  the  time  from  now  to  mid- 
night.    What  is  the  hour?    Ans. :  4  o'clock  p.  m. 

3.  What  is  the  time  of  day  if  the  time  past  noon  is  j\  of  the 

time  past  midnight  ?    Ans.  :  10  o'clock  p.  m. 

4.  What  is  the  time  of  day  if  the  time  past  noon  is  x\-  of  the 

time  to  midnight  ?    Ans.  :  45  min.  past  3  p.  m. 

5.  \  of  the  time  past  noon  equals  ^^  of  the  time  to  mid- 

night.   What  is  the  time  ?    Ans.  :  4  o'clock  p.  m. 

6.  At  what  time  between  7  and  8  o'clock  are  the  hour  and 

minute  hands  together?    Ans.  .  "^yx  inin.  after  7. 

7.  What  is  the  time  of  day  when  f  of  the  time  past  noon 

equals  2*^9  of  the  time  to  12  ?    Ans.  :  2\  p.  m. 

8.  If  I  of  the  time  past  noon  equals  /^  of  the  time  to  mid- 

night, what  is  the  time?    Ans.:  i7y  min.  after  4  p.  m. 

9.  What  is  the  time  of  day  when  f  of  the  time  past  noon 

equals  jVj  of  the  time  to  the  second  midnight  ?    Ans.  : 
i|^  o'clock  A.  M. 

ID.   If  ^  of  the  time  past  midnight  equals  \  of  the  time  to 
midnight,  what  is  the  hour?    Ans.:  8  o'clock  p.  m. 

11.  If  the  time  past  noon  increased  by  90  min.  equals  j\  of 

the  time  from  noon  to  midnight,  what  is  the  time? 
Ans.  :  57tt  ™i"-  P^st  3  p.  m. 

12.  When  the  hour  hand  is  22  min.  ahead  of  the  min.  hand, 

how  far  must  the  min.  hand  go  to  overtake  the  hour 
hand  ?    Ans.  :  24  min. 

13.  At  what  time  between  9  and  10  will  the  hour  hand  be  i 

minute-space  behind  the  minute  hand  ?    Ans.  :  9i\  min. 
before  lo  o'clock. 


APPLICATION  OF  SQUARE  ROOT.  59 

14.  At  what  time  between  10  and  11  o'clock  are  the  hands  of 

a  clock  opposite  ?    Ans.  :  2ij\  past  10. 

15.  At  what  time  between  4  and  5  o'clock  are  the  hour  and 

minute  hands  10  minutes  apart?    Ans.  :  32 j\  min.  past 
4  and  \o\\  min.  past  4. 

i6.  At  what  time  between  8  and  9  is  the  minute  hand  midway 
between  twelve  and  the  hour  hand?  When  is  the  hour 
hand  as  far  behind  the  minute  hand  as  it  is  past  6? 
Ans.  :  2o|f  min.  past  8 ;  and  60  min.  past  8,  or  9  o'clock. 

17.  At  what  time  between  5  and  6  o'clock  is  the  hour  hand 

midway   between  4  and  the  minute  hand  ?    Ans.  :    36 
min.  after  5. 

18.  The  time  past  noon  is  y^  of  the  time  to  4  o'clock  P.  M. 

What  is  the  time  ?    Ans.  :  i^  o'clock  p.  m. 


APPLICATION  OF  SQUARE  ROOT, 


1.  Find  the  side  of  a  square  field  containing  one  acre.    Ans.  : 

12.64+rds. 

2.  Find  the  side  of  a  square  field  containing  10  acres.    Ans.  : 

40  rds. 

3.  What  will  the  lumber  cost  that  will  fence  a  square  field, 

5  rails  high,  containing  10  acres,  with  post  and  rail  fence, 
allowing  15  ft.  to  the  panel,  rails  at  $6  a  hundred  and 
posts  $40  a  hundred  ?     Ans.  :  $123.20. 

4.  The  entire  surface  of  a  cubical  block  is  216  sq.  ft.     What 

is  the  side  of  one  face?    Ans.  :  6  in. 

5.  How  long  must  a  tape-line  be  to  wind  spirally  around  a 

cylinder  that  is  50  ft.  long  and  8  ft.  in  circumference,  if 
it  pass  once  around  in  every  6  ft.  of  the  cylinder's 
length?    Ans.:  83 J  ft. 


6o  APPLICATION  OF  CUBE  ROOT. 


6.  Two  freight  traius  ^tart  at  the  same  point,  one  going  due 

south  at  the  rate  of  15  miles  an  hour,  and  the  other  due 
east  at  the  rate  of  18  miles  an  hour.  How  far  apart 
were  they  at  the  end  of  6  hrs.  ?    Ans.  :  i4o.58-t-niiles. 

7.  What  is  the  distance  around  a  rectangular  field  containing 

20  acres  whose  length  is  twice  its  breadth  ?  Ans.  :  240 
rds. 

8.  The  area  of  a  rectangle  is  5,408  sq.  ft.,  and  is  composed  of 

two  squares.  What  is  the  length  of  its  sides  ?  Ans.  : 
52  ft.  wide,  104  ft.  long. 

9.  A  room  is  100  ft.  long,  60  ft.  wide  and  26  ft.  high.     What 

is  the  distance  from  a  lower  corner  to  the  opposite  up- 
per corner  ?    Ans.:  119.48-)- ft. 

10.   Hypotenuse  50 ;  the  base  and  perpendicular  equal.     Find 
them.    Ans.:  35.35+. 


APPLICATION  OF  CUBE  ROOT. 


1.  A  cubical  box  holds  one  bu.    What  is  the  inside  measure*,  ? 

Ans.:  i2.9-j-in. 

2.  The  volume  of  a  cube  is  15!  cu.  ft.     Find  its  surface  in 

sq.  in.     Ans.  :  5,400  sq.  in. 

3.  Find  the  difference  between  6  cu.  in.  and  a  6  in.  cube. 

Ans.  :  210  cu.  in. 

4.  What  is  the  size  of  a  cubical  cistern  which  holds  1,500  gal, 

of  water?    Ans. :  70.234-cu.  in. 

5.  What  are  the  dimensions  of  a  cubical  pile  of  wood  whicn 

contains  80  cords  ?    Ans.  :  21.71-l-ft. 

6.  What  are  the  dimensions  of  a  cellar,  from  which  192  cubic 

yds.  of  earth  were  removed,  if  the  length  is  4  times  and 
the  width  6  times  its  depth  ?    Ans.  :  6,  24  and  36  ft. 


MEASUREMENTS.  6i 


7.  A  stick  of  timber  contains  13J  cu.  ft.     Its  length  is  32 

times  its  width   or  thickness.     Find    its   dimensions. 
Ans.  :  24  ft.  long  and  9  in.  square. 

8.  A  cubical  box  has  a  capacity  of  2,048  cu.  ft.     What  are  the 

dimensions  of  4  equal  cubical  boxes  that  can  be  placed 
in  it.?    Ans.:  8  ft. 

9.  I  have  8  boxes  containing  729  cu.  ft.  each.    What  is  the 

side  of  a  cubical  box  equal  in  capacity  to  the  8  ?    Ans.  : 
18  ft. 

10.  I  wish  to  make  a  wagon  bed  to  hold  100  bu.,  the  length 
being  3  times  the  width  and  height.  What  will  be  the 
dimensions  1    Ans.  :  3.46-J-ft.  high ;  10.38-f-length. 


MEASUREMENTS. 


1.  What  is  a  cylindrical  stack  of  clover  hay  worth  that  is  12  ft. 

in  diameter  and  10  ft.  high  at  $15  a  ton  ?    Ans.  :  $30.84-1-. 

2.  How  much  timothy  hay  will  a  mow  hold  that  is  20  ft. 

square  and  15  ft.  deep?    Ans.  :  13J  tons. 

3.  How  much  clover  hay  in  a  mow  that  is  30  ft.  long,  20 

ft.  wide  and  20  ft.  deep  ?    Ans  :  2Iy\  tons. 

4.  I  have  12  bins,  each  10  by  5  and  8  ft.  deep,  full  of  wheat. 

How  many  bu.  of  wheat  have  I .?    Ans.  :  3,840  bu. 

5.  How  many  gallons  in  a  barrel  whose  capacity  is  6.25  cu. 

ft.?    Ans.:  46.75-l-gal. 

6.  How  many  bu.  of  wheat  in  a  box  containing  750  cu.  ft.  ? 

Ans.  :  600  bu. 

7.  I  have  a  wagon-bed  that  holds  135  bu.     What  are  its  di- 

mensions if  the  length  is  six  times  its  width  and  9  times 
its  depth  ?    Ans.  :  18  ft.  long,  3  ft.  wide  and  2  ft.  deep. 

8.  A  cubical  box  holds  583.2  bu.    What  are  its  dimensions? 

Ans.  :  9  ft. 


62  MEASUREMENTS. 

9.  How  many  bags  holding  i^  pk.  eacli  can  be  filled  from  a 
bin  of  wheat  which  is  10  ft.  long,  4  ft.  wide  and  8  ft. 
deep  ?    Ans.  :  768  bags. 

10.  What  will  it  cost  to  build  a  stone  wall  80  ft.  long,  2\  ft. 

thick  and  10  ft.  high  at  $1  a  perch  ?    Ans.  :  $8o||. 

11.  I  paid  $254.54y^x  fo^  the  cellar  wall  of  my  house,  60  ft.  by 

45  ft.     The  wall  was  8  ft.  high  and  i\  ft.  thick.     What 
did  I  pay  a  perch  ?    Ans.  :  $2.50. 

12.  What  will  a  log  cost  that  is  20  ft.  long  and  average  girt  60 

in.  at  2\  cts.  a  cu.  ft.  ?    Ans.  :  99.5+cts. 

13.  What  is  the  number  of  feet  of  lumber  in  a  stick  of  timber 

20  ft.  long,  8  in.  wide  and  4  in.  thick  ?    Ans.  :  53^^  ft. 

14.  How  many  feet  in  12  boards  16  ft.  long  and  15  in.  wide  ? 

Ans.:  240. 

15.  What  is  the  largest  cube  that  can  be  cut  from  a  sphere  30 

in.  in  diameter ?    Ans.:  17.324-iii. 

16.  A  globe  40  in.  in  diameter,  the  shell  beirg  i  in.  thick,  is 

filled  with  water.     How  many  gallons  are  in  it?    Ans.  : 
124.37+gal. 

17.  What  will  it  cost  to  guild  a  globe  60  in.  in  diameter  at  2 

cts.  a  square  inch?    Ans.:  1226.195+. 

18.  If  it  cost  $1005.312  to  guild  a  globe  at  5c.  a  sq.  in.,  what  is 

its  diameter  ?    Ans.  :  80  in. 

19.  I  paid  $226,195  to  have  a  globe  60  in.  in  diameter  gilded. 

What  was  the  price  per  sq.  in.  ?    Ans.  :  2  cts. 

20.  What  will  it  cost  to  have  a  cube  whose  sides  are  2  in. 

plated  with  silver  at  50  cts.  per  sq.  in.  ?    Ans.  :  $12. 

21.  How  many  cubic  ft.  in  20  posts  12  ft.  long,  6  in.  square  at 

one  end  and  4  by  4  at  the  other?    Ans.  :  42f  cu.  ft. 

22.  How  many  cu.  ft.  in  a  log  40  ft.  long,  3  ft.  in  diameter  at 

one  end  and  2  ft.  at  the  other?    Ans.  :  198.968-I-. 

23.  A  water  tank  in  the  shape  of  a. frustum  of  a  cone  is  15 

ft.  deep,  the  lower  diameter  is  16  ft.  and  the  upper  12 
ft.     Find  the  contents.     Ans.  :  2,324.65-f-cu.  ft. 

24.  How  many  cu.  ft.  in  the  frustum  of  a  square  pyramid  of 

stone    20   ft.  high  ;  the  side  of  the  upper  base  is  8  in. 
and  thfe  lower  base  20  in  ?    Ans.  :  28|  cu.  ft. 


MEASUREMENTS,  63 

25.  The  slant  height  of  the  frustum  of  a  square  pyramid  is 

10  ft.    The  side  of  the  upper  base  is  20  in.  and  the 
lower  30  in.    Find  the  convex  surface.    Ans.  :  83J  sq.  ft 

26.  I  sold  a  block  of  marble  20  ft.  long  and  20  in.  square  at 

each  end  at  $2.25  per  cu.  ft.    What  did  I  receive  for  it  ? 
Ans.:  $125. 

27.  The  base  of  a  square  pyramid  is  764  ft.  on  each  side ;  height 

480  ft.    What  is  the  solidity  ?    Ans.  :  93,391,360  cu.  ft. 

28.  The  slant  height  of  a  square  pyramid  is  8  ft.  and  the  sides 

of  the  base  5  ft.    Find  the  entire  surface.    Ans.  :  125 
sq.  ft. 

29.  If  I  receive  $140.80  for  painting  an  octagonal  church  spire 

whose  slant  height  is  80  ft.  and  the  sides  of  its  bases  8 
ft.,  what  do  I  receive  a  sq.  ft.  ?    Ans.  :  ^\  cts. 

30.  What  will  it  cost  to  paint  a  cone  whose  slant  height  is  60 

ft.  and  the  circumference  of  its  base  40  ft.,  at  5  cts.  a 
square  foot  ?    Ans.  :  |6o. 

31.  How  many  gallons  will  a  cistern  hold  that  is  20  ft.  deep 

and  30  ft.  in  diameter  ?    Ans.  :  105,753!  gal. 

32.  A  log  50  ft.  long  and  2  ft.  thick  was  sold  at  20  cts.  a  cu.  ft. 

What  did  it  cost  ?    Ans.  :  $31.41-!-. 

33.  I  sold  a  log  i\  ft.  in  diameter  at  10  cents  a  cu.  ft.  and  re- 

ceived $3,927.    What  was  its  length  ?    Ans.  :  8  ft. 

34.  A  square  stick  of  timber  60  ft.  long  at  20  cents  a  cu.  ft. 

cost  $27.     How  many  ft.  of  inch  plank  will  it  make,  al- 
lowing \  waste  for  sawing  ?    Ans.  :  1,440  ft. 

35.  I  paid  $3.31^  for  painting  the  sides  and  one  end  of  a  rect- 

angular prison  6  ft.  high  and  the  sides  2  J  ft.  each.    What 
did  I  pay  a  square  foot  ?    Ans.  :  5  cts. 

36.  How  large  a  square  can  be  placed  in  a  circle  whose  diame- 

ter is  3  ft.  ?    Ans.  :  25.455+in. 

37.  A  circular  island  is  14  rds.  in  diameter.    What  is  the  value 

of  the  largest  inscribed  square  at  $2  per  sq.  rd.  ?    Ans.  : 
$196. 

38.  The  circumference  of  a  circular  pond  is  one  mile.    What 

is  its  diameter  ?    Ans.  :  1,680. 674-ft. 


^4  MEASUREMENTS. 


39.  What  is  the  area  of  a  circular  field  inclosed  by  one  mile 

of  fence  ?    Ans.  :  50  acres  148  perches  188.39-l-sq.  ft. 

40.  A  circular  fish  pond  100  ft.  in  diameter  was  sold  at  10  cts. 

a  sq.  ft.    What  did  it  bring  ?    Ans.  :  $785.40. 

41.  A  horse  tied  by  a  rope  grazed  over  7854  sq.  ft.     How  long 

was  the  rope  ?    Ans.  :  50  ft. 

42.  Two  boys  in  rowing  across  a  stream  620  ft.  wide  go  800  ft. 

How  far  did  they  drift  ?    Ans.  :  505.57+ft. 

43.  A  rope  40  ft.  long  tied  to  the  top  of  a  house  reaches  10  ft. 

in  the  street.    How  high  is  the  house  ?    Ans.  :  38,72-j-ft. 

44.  What  will  it  cost  to  paint  a  steam  boiler  30  ft.  long  and  5 

ft.  in  diameter  at  2  cts.  a  sq.  ft.,  allowing  10  sq.  ft.  for 
openings  ?    Ans.  :  $io.oi-|-. 

45.  A  cistern  holds  20  hhds.  and  is  5  ft.  10  in.  in  diameter. 

What  is  its  depth  ?    Ans.  :  6  ft.  3.63-i-in. 

46.  If  a  pint  of  water  will  fill  15  cone-shaped  glasses,  how 

many  times  will  a  gallon  fill  similar  glasses  of  i^  times 
the  diameter  at  the  top  ?    Ans.  :  53J. 

47.  How  many  square  inches   on    a  school   globe   15  in.  in 

diameter?    Ans.:  706.86. 

48.  What  is  the  diameter  of  a  tin  pan  whose  area  is  196  sq.  in.  ? 

Ans.:  15.79+in. 

49.  The  radius  of  a  circle  is  11  ft.    What  is  the  area?    Ans.  : 

380.133+sq.  ft. 

50.  I  paid  $76.80  for  the  flooring  of  a  two-story  house  24  x  32 

ft.     What  did  I  pay  for  every  hundred  ft.  ?    Ans.  :  $5. 

51.  What  will  be  the  cost  of  9  boards  13  ft.  long,  9  in.  wide 

and  i\  in.  thick  at  $1  a  hundred  ?    Ans.:  $1.31-!-. 

52.  The  surface  of  a  globe  is  1520.5344  sq.  ft.     Find  the  diame- 

ter.   Ans.:  22  ft. 

53.  What  is  the  surface  of  a  globe  whose  circumference  is 

39.27  in.?    Ans.  :  490.875  sq.  in. 

54.  The  solidity  of  a  sphere  is  65.45  cu.  in.     Find  the  surface. 

Ans.:  78.54  sq.  in. 

55.  What  is  the  solidity  of  a  globe  wh«se  diameter  is  \\  ft.  ? 

Ans.:  I  cu.  ft.  391.5  cu,  in. 


MISCELLANEOUS.  65 


56.  Over  what  area  can  a  horse  graze,  tied  by  a  rope  52  ft.  long 

to  the  top  of  a  stake  20  ft.  high  ?    Ans.  :  26.58-j-sq.  rds. 

57.  Find  the  curved  surface  of  a  right  cone  whose  base  is 

4  ft.  in  diameter  and  slant  height  5  ft.     Ans.  :    31.41-I- 
sq.  ft. 

58.  The  sides  of  a  triangle  are  10,  10^  and  14^.     What  is  the 

area.?    Ans.  :  52.5. 

59.  The  base  of  a  triangle  is  136,  altitude   17.     What  is  the 

side  of  a  square  equal  in  area?    Ans.  :  34. 

60.  How  much  paper  2  ft.  wide  will  it  take  to  cover  the  walls 

of  a  room  16  ft.  long,  14  ft.  wide  and  8  ft.  high  ?    Ans.  : 
80  yds. 

61.  My  cistern  is  5J  ft.  deep  and  6  ft.  in  diameter  at  the  top 

and  6  ft.  at  the  bottom.     How  many  barrels  will  it  hold  ? 
Ans.:  35.254-bbls. 

Note.— The  answers  to  a  few  of  the  above  problems,  such  as  finding 
the  capacity  of  wagon  beds,  etc.,  are  only  approximately  correct. 


MISCBLIvANEOUS. 


1.  A  tree  100  ft.  high  was  broken  by  the  wind  so  that  the 

top  reached  the  ground  30  ft.  from  the  stump.  How 
high  is  the  stump  ?     Ans.  :  45^  ft. 

2.  What  is  the  least  number  of  squares  of  the  greatest  pos- 

sible size  contained  in  a  field  40  by  30  rds,  ?    Ans.  :    12. 

3.  If  the  diameter  of  a  ball  whose  volume  is  27  cu.  in.  is 

3  in.,  what  is  the  diameter  of  a  ball  whose  volume  is 
343CU.  in.?    Ans.:  7  in. 

4.  A  grocer  at  one  straight  cat  took  off  a  segment  of  cheese 

which  had  \  of  the  circumference  and  weighed  3  lbs. 
What  is  the  weight  of  the  whole  cheese?  Ans.:  33.02 
+lbs. 


66  MISCELLANEOUS. 


5.  If  a  pipe  i^  in.  in  diameter  fill  a  cistern  in  5  hrs.,  in  what 

time  will  a  pipe  3  in.  in  diameter  fill  the  same  cistern? 
Ans.  :  i|^  hrs. 

6.  Three  poles,  each  50  ft.  long,  are  tied  together  at  the  top 

and  stand  60  ft.  apart  at  the  base  ;  what  is  the  distance 
from  the  apex  to  the  ground?    Ans.  :  38.73-}- f^- 

7.  The  diagonal  of  a  field  in  the  shape  of  a  parallelogram 

containing  30  acres  is  100  rds.  Find  the  sides.  Ans.  : 
80  and  60  rds. 

8.  The  base  of  a  triangle  is  9  in.     What  will  be  the  length 

of  a  line  drawn  parallel  with  the  base  so  as  to  divide  it 
into  two  equal  parts  ?    Ans.  :  6.36-l-in. 

9.  What  integer  multiplied  by  the  next  greater  gives  1,332  ? 

Ans.:  36. 

10.  What  integer  is  that  whose  square  root  is  5  times  its  cube 

root?    Ans.:  15,625. 

11.  What  is  the  side  of  a' square  field  whose  diagonal  is  10 

rods  longer  than  its  side  ?     Ans.  :  24.14-f-rds. 

12.  How  much  square  edged  inch  lumber  can  be  cut  from  a 

log  32  in.  in  diameter  and  20  ft.  long  ?    Ans.  :  980  ft. 

13.  The  side  of  a  square  field  containing  18  acres  is  53.6-f-rds. 

What  is  the  side  of  a  similar  field  that  contains  \  as 
much  ?    Ans.  :  30.9-{-rds. 

14.  What  is  the  side  of  the  largest  cube  that  can  be  cut  from 

a  globe  36  in.  in  diameter  ?    Ans.  :  20-|-in. 

15.  How  much  wheat  will  a  cubical  box  hold  whose  diagonal 

is  12  ft.  ?    Ans.  :  2664-bu. 

16.  The  perpendicular  and  base  of  a  right-angled  triangle  are 

equal  and  its  area  is  8  acres.  What  is  the  hypotenuse  ? 
Ans.:  71.5+rd. 

17.  The  base  of  a  triangle  is  136,  the  altitude  17.     Find  the 

side  of  a  square  equal  in  area.    Ans.  :  34. 

18.  Two  poles  are  of  equal  length.     When  one  is  placed  up- 

right and  the  other  is  leaning  against  it,  their  tops  are 
4  ft.  asunder  and  their  feet  are  16  ft.  apart.  What  is  the 
length  of  each  ?    Ans.  :  34  ft. 


MISCELLANEOUS.  67 

19.  A  board  \\  inches  thick  contains  49I  sq.  ft.    What  is  the 

side  of  the  largest  cubical  box  that  can  be  made  from 
it?    Ans.  :  36  in. 

20.  How  many  acres  in  an  equilateral  triangle  each  side  of 

which  is  one  furlong  in  length  ?    Ans.  :  4. 334- A. 

21.  If  Ihc  diameter  of  the  greater  of  two  concentric  circles  be 

30  ft,,  and  that  of  the  smaller  20,  what  is  the  area  of 
the  space  between  them?    Ans.  :  392.7-l-sq.  ft. 

22.  The  length  of  a  field  containing  4  A.  is  12  rds,  longer  than 

its  side.  What  is  the  length  and  breadth?  Ans.:  20 
and  32  rd. 

23.  It  is  required  to  inclose  a  piece  of  ground  with  a  fence  10 

rails  high,  2  panels  to  the  rod,  and  to  have  just  as  many 
acres  inclosed  as  there  are  rails  in  the  fence.  How 
many  acres  in  the  field,  the  field  being  square  ?  Ans.: 
1,024,000  A. 

24.  How  many  square  inches  of  leather  will  cover  a  ball  3J 

in.  in  diameter  ?    Ans.  :  38.4-l-sq.  in. 

25.  A  man  was  hired  50  days  on  condition  that  for  every  day 

he  worked  he  should  receive  75c.,  and  should  pay  25c. 
for  every  day  he  was  idle.  On  settlement  he  received 
$27.50 ;  how  many  days  was  he  idle  ?    Ans.  :  10. 

^6.  Divide  120  apples  among  3  boys,  and  as  often  as  the  first 
shall  receive  3,  give  the  second  5,  and  the  third  7  ;  what 
will  be  the  share  of  each  ?     Ans.  :  24,  40  and  56. 

27.  Three  men  bought  a  grindstone  30  in.  in  diameter,  each 

paying  the  same.  They  grind  off  their  shares  succes- 
sively. Find  the  thickness  of  each  man's  share.  No 
aperture.     Ans.:  ist,  2.75+;  2d,  3.59-I- ;  3d,  8.65-f. 

28.  A  circuit  is  20  miles  in  circumference.     A  goes  2  miles  an 

hr.,  B  4,  and  C  6  ;  they  start  at  the  same  point ;  how  long 
will  it  be  before  they  meet  ?     AnS.  :  10  hrs. 

29.  \  the  number  of  dollars  in  a  purse  exceeds  J  by  20 ;  what 

does  the  purse  contain  ?    Ans.  :  $240. 

30.  The  head  of  a  fish  is  10  in.  long,  its  tail  is  as  long  as  its 

head  and  \  the  body,  and  the  body  as  long  as  the  head 
and  tail  both.    How  long  is  the  fish  ?    Ans.  :  80  in. 


68  MISCELLANEOUS. 


31.  A  and  B  together  can  do  a  piece  of  work  in  18  days.     A 

alone  can  do  it  in  30  days ;  in  what  time  could  B  do  it 
alone?    Ans.:  45  days. 

32.  Suppose  the  radius  of  the  earth  is  4,000  miles;  what 

would  a  20  lb.  ball  weigh  3  miles  from  the  surface  of 
the  earth  .>    Ans.  :  19.97-hlbs. 

33.  In  what  time  will  a  leaden  ball  drop  from  a  steeple  484 

feet  high  ?    Ans.  :  5J  seconds. 

34.  A  ball  discharged  directly  upwards  returns  to  the  earth 

in  12  seconds  ;  how  high  did  it  ascend  ?    Ans.  :  576  ft. 

35.  A  stone  let  fall  reaches  the  bottom  of  a  well  in  2  seconds; 

how  deep  is  the  well  ?    Ans.  :  64  ft. 

36.  If  a  scaffold  20  ft.  square  holds  50  bu.  of  fruit,  how  many 

bu.  will  one  30  ft.  square  hold  ?    Ans.  :  112  J  bu. 

37.  What  is  the  diameter  of  each  of  the  3  largest  equal  cir- 

cles that  can  be  inscribed  in  a  circular  farm  containing 
500  acres?     Ans.:  148.14-rds. 

38.  If  cloth  for  a  suit  of  clothes  for  a  man  weighing  125  lbs. 

cost  $10,  what  will  it  cost  to  make  a  suit  for  a  man 
weighing  216  lbs.  ?    Ans.  :  $14.40. 

39.  I  am  45  yrs.  of  age.     How  many  yrs.  old  would  I  be  if  I 

had  lived  the  same  length  of  absolute  time  on  the 
planet  Mercury?  On  Jupiter?  Ans.:  Mercury  186.8 
yrs.  old ;  Jupiter  .53  or  a  little  past  \  yr.  old. 

40.  A  and  B  shot  by  turns  at  a  target ;  A  put  7  balls  out  of  12 

in  the  center,  and  B  3  out  of  4,  and  between  them  they 
put  in  32  balls.    How  many  shots  did  each  fire  ?   Ans.  :  24. 

41.  From  the  middle  of  the  side  of  a  square  lo-acre  field  a 

line  is  run  cutting  off  i|^  acres.  What  is  the  length  of 
the  line  ?    Ans.  :  36-f-rods. 

42.  A  tube  \  in.  in  diameter  will  empty  a  cistern  in  50  min. 

In  what  time  will  it  empty  it  when  another  pipe  \  of  an 
inch  in  diameter  is  running  into  it  ?    Ans.  :  623-%  min. 

43.  Three  equal  circles  touch  each  other  externally,  thus  in- 

closing one  acre.  What  is  the  diameter  of  each  circle  ? 
Ans.:  63-f-rds. 


MISCELLANEOUS.  '  69 


44.  What  are  the  sides  of  a  right-angled  triangle  having  the 

least  hypotenuse  in  which,  if  a  square  be  inscribed,  its 
side  will  be  12  ?    Ans.  :  24. 

45.  If  the  arch  line  of  a  sector  measures  5  ft.  and  the  radius 

4  ft.,  what  will  be  the  area  ?    Ans.  :  10  ft. 

46.  I  bought  a  6  per  cent.  $2,500  mortgage  at  5  per  cent,  dis- 

count, with  two  yrs.  to  run  ;  prove  that  I  get  8|f  per 
cent,  interest  on  the  money  invested,  the  mortgage  be- 
ing satisfied  at  maturity. 

47.  Required  the  number  of  acres  in  a  field  whose  length  is 

to  its  breadth  as  4:5,  having  a  fence  around  it  7  rails 
high,  two  panels  to  the  rod,  and  just  as  many  rails  as 
acres.     Ans.  :  508,032. 

48.  The  perpendicular  of  a  right-angled  triangle  is  36  ft.,  and 

the  sum  of  the  other  sides  is  108  ft.  Find  them.  Ans.: 
Base,  48  ft. ;  hypotenuse,  60  ft. 

49.  A  square  field  has  an  area  of  10,000  sq.  yds.     What  is  the 

breadth  of  a  walk  around  it,  that  the  area  of  the  walk 
is  Y^^  of  the  area  of  that  part  within  the  walks  ?  Ans.  : 
10  yds. 

50.  Two  ladders  are  standing  in  a  street  with  their  bases  20 

ft.  apart,  inclined  toward  each  other,  at  an  angle  of  45 
degrees  until  their  tops  intersect.  What  is  their  length  ? 
Ans.:  14.14-hft. 

51.  A  cube  of  lead  whose  side  was  4  inches  was  evenly  plated 

with  61  cu.  in.  of  silver ;  how  thick  was  the  plating  ? 
Ans.  :  \  inch. 

52.  A  bicycle  wheel  makes  840J  revolutions  to  the  mile ;  what 

is  the  height  of  the  wheel  ?    Ans.  :  2  ft. 

53.  A  tower  is  195  ft.  high  and  10  ft.  in  diameter  at  the  top. 

To  a  man  whose  eye  is  5  ft.  above  the  center  of  the  top 
of  the  tower,  what  area  of  the  street  will  be  hid  ?  Ans.  : 
502,656  sq.  ft. 

54.  How  much  inch  rope  will  be  required  to  go  round  a  stove- 

pipe I  ft.  in  diameter  so  that  the  outer  edges  will  meet  ? 
Ans.  :  43.984-in. 

55.  Mt.  St.  Elias  is  19,283  feet  high.     At  what  distance  on  the 

Pacific  Ocean  may  its  top  be  seen  ?    Ans.  :  169.9-l-niiles. 


^6  MISCELLANEOUS. 

56.  A  rectangular  piece  of  ground  containing  \  an  acre  is  5 

times  as  long  as  it  is  broad.  What  is  the  length  and 
breadth  ?    Ans.  :  4  and  20  rods. 

57.  A  had  hired  for  a  year  at  $168  and  5  cords  of  wood  ;  he  left 

in  7^  months  and  received  $98  and  the  wood.  What 
was  the  wood  worth  per  cord  ?    Ans.  :  $1.40. 

58.  How  much  gold  90^  pure  must  be  mixed  with  24  oz.  65^ 

pure  to  make  the  mixture  80%  pure  .?    Ans.  :  36  oz. 

59.  Yesterday  at  noon  my  longitude  was  16°  18^  west.    To-day 

the  sun  came  on  the  meridian  at  ii  o'clock  and  36  min. 
What  is  my  longitude  ?    Ans.  :  10°  18^  west. 

60.  I  have  a  mirror  12  by  36  in.,  and  its  frame  of  uniform 

width  contains  448  sq.  in.  How  wide  is  the  frame? 
Ans.  :  4  in. 

61.  A  ladder  placed  8  feet  from  a  wall  just  reaches  the  top  of 

the  building  40  ft.  high.  How  far  must  it  be  placed 
from  the  wall  to  reach  a  point  10  ft.  from  the  top? 
Ans.:  27.64-l-ft. 

62.  A  room  in  the  shape  of  a  cube  measures  20  ft.  on  each 

side.  How  far  is  it  from  each  upper  corner  to  the  cen- 
ter of  the  floor  ?    Ans.  :  24.49+ ft. 

63.  A  sc[uare  field  is  of  such  size  that  if  silver  dollars  i^  in.  in 

diameter  are  laid  around  the  boundary  so  they  will  touch 
each  other  they  will  pay  for  the  land  at  $40  per  acre. 
How  many  acres  in  the  field  ?    Ans.  :  27,878!  acres. 

64.  A  rifle  ball  fired  perpendicular  in  the  air  returned  to  the 

ground  in  16  sec.     How  far  did  it  go  ?    Ans.  :  1,024  *t. 

65.  There  is  a  park  16  rods  square.     I  make  a  path  around 

the  edge  containing  ^|  of  the  area  of  the  park.  How 
wide  is  the  path  ?    Ans.  :  i  rod. 

66.  A  man  weighs  160  lbs.  av.     What  will  he  weigh  troy? 

Ans.  :  194-f-lbs. 

67.  A  fence  5  boards  high,  each  board  6  in.  wide,  is  built 

around  a  lo-acre  square  field.  What  is  the  lumber 
worth  at  $8  per  M  ?    Ans.  :  $52.80. 

68.  A  regular  octagon  has  a  perimeter  96  ft.,  and  the  distance 

from  the  center  to  the  middle  of  each  side  is  12  ft 
Find  the  area.     Ans  :  576  fq.  ft. 


MISCELLANEOUS.  71 

69.  What  is  a  field  worth  in  the  shape  of  a  triangle  and  the 

sides  in  proportion,  as  6,  8  and  10,  the  shorter  side  be- 
ing 12  rds.,  at  $850  per  acre  ?    Ans.  :  $510. 

70.  A  boat  can  go   15  mi.  per  hr.  down  stream  and  10  miles 

per  hr.  up  stream.     How  far  can  it  go  and  return  in 
4  hours  ?    Ans.  :  24  miles. 

71.  How  much  more  water  will  a  tile  6  in.  in  diameter  dis- 

charge per  hr.  than  one  4  in.  ?    Ans.  :  i\  times. 

72.  A,  B  and  C  dine  on  6  pies.     A  furnishes  4  and  B  2.    C  pays 

10  cents  for  his  dinner.     How  shall  A  and  B  divide  the 
money  ?    Ans.  :  A  gets  10  cts. 

73.  What  is  the  diameter  of  a  sphere  whose  volume  is  equal 

to  a  cone  whose  base  is  i  ft.  in  diameter  and  altitude  2 
ft.  ?    Ans.  :  I  ft. 

74.  How  many  bu.  of  coal  will  a  cart  hold  that  is  9J  ft.  long, 

3 J  ft.  wide,  13  in.  deep  ?    Ans.  :  24-l-bu. 

75.  How  long  will  it  take  $50  to  amount  to  $72.50  at  8J%? 

Ans.  :  5  yrs.  3  mo.  16  da. 

76.  If  the  time  past  noon  plus  i^  hrs.  is  -f^  of  the  time  from 

noon  to  midnight,  what  is  the  hour  ?    Ans.  :  3J  o'clock 
p.  M. 

77.  If  a  cistern  5  ft.  in  diameter  and  10  ft.  deep  holds  500  bbls., 

how  many  bbls.  will  a  cistern  10  ft.  in  diameter  and  20 
ft.  deep  hold  ?    Ans.  :  4,000  bbls. 

78.  How  many  feet  of  lumber  in   a  stick  of  timber  18  in. 

square  at  one  end,  6  in.  square  at  the  other  and  20  ft. 
long  ?    Ans.  :  260  ft. 

79.  How  much  lumber  in  a  pole  20  ft.  long  and  10  and  5  in. 

in  diameter  respectively  ?    Ans.  :  7.7-l-sq.  ft. 

80.  If  a  man  5  ft.  high  weigh  120  lbs.,  what  will  a  man  6  ft. 

high  weigh  ?    Ans.  :  207-l-lbs. 

8r.   If  a  piece  of  gold  weigh  9  oz.  in  the  air  and  8 J  oz.  in  the 
water,  what  is  its  specific  gravity  ?    Ans.  :  18. 

82.  A  cube  has  an  area  of  5,400  sq.  in.     What  is  its  solid  con- 

tents?   Ans.:  27,000  cu.  in. 

83.  I  can  pasture  12  horses  or  15  cows.     How  many  horses  can 

I  keep  if  I  have  10  cows  ?    Ans.  :  4. 


72  MISCELLANEOUS. 

84.  A  can  do  a  piece  of  work  in  80  days,  B  in  40  days  ;  both 

together  work  12  days,  then  B  quits  but  returns  in  time 
for  them  to  complete  the  work  in  40  days.  When  did 
B  return  ?    Ans.  :  End  of  32d  day. 

85.  The  extreme  point  of  a  minute  hand  of  a  clock  moves  30 

in.  in  12  minutes.    How  long  is  the  hand  ?    Ans.  :  23-|-iti. 

86.  A  man  hired  for  80  days  at  $3  per  day ;  he  spent  $r  every 

day  he  was  idle;  at  the  end  of  that  time  he  had  $150. 
How  many  days  did  he  work?    Ans.  :  57^. 

87.  A  cistern  5  ft.  in  diameter  holds  100  bbls.  of  water.     What 

will  one  of  the  same  depth  and  \2\  ft.  in  diameter  hold? 
Ans.  :  625  bbls. 

88.  A  pyramid  is  10  ft.  square  at  the  base  and   20  ft.  high. 

How  far  from  the  base  must  it  be  divided  parallel  to  the 
base  to  make  two  equal  parts  ?    Ans.  :  4.«2 — ft. 

89.  If  a  hay  stack  20  ft.  high  contains  10  tons,  what  will  a 

similar  one  10  ft.  high  contain  ?    Ans.  :  i^  tons. 

90.  Find  the  length  of  an  hour  hand  of  a  clock,  whose  ex- 

treme point  moves  2  in.  in  15  minutes.    Ans.  :  i5-|-in. 

91.  Two  men  carry  a  hog  weighing  200  lbs.  with  a  stick  6  ft. 

long.  What  weight  does  each  sustain  if  it  is  6  in.  from 
the  center  of  the  stick?    Ans.  :  83 J  and  ii6f  lbs. 

92.  A,  B  and  C  buy  a  grindstone  3  ft.  in  diameter  for  $5.00.    A 

pays  $2,  B  $1.75,  C  $1.25.  How  much  must  each  grind 
off  to  get  his  deserved  share  ?  A  grinds  first,  B  second 
and  C  last.    Ans.  :  A,  4064-;  B,  355+  ;  C,  2544-sq.  in. 

93.  How  much  water  must  be  mixed  with  vinegar  worth  40 

cts.  a  gal.  to  make  50  gal.  of  the  mixture  worth  25  cts. 
a  gal.  ?    Ans.  :  i8|  gal. 

94.  If  a  cu.  ft.  of  iron  was  made  into  a  bar  \  in.  square,  what 

would  be  its  length  ?    Ans.  :  2,304  ft. 

95.  Find  the  sides  of  a  rectangular  field  containing  200  acres, 

one  side  being  40  rods  longer  than  the  adjacent  side. 
Ans.  :  160  and  200  rds. 

96.  Find  the  cost  of  a  fence  at  $3  per  rd.  that  will  enclose  a 

square  field  of  20  acres.    Ans.  :  $678. 

97.  How  many  sq.  yds.  of  canvas  will  be  required  to  make  a 

tent,  diameter  24  ft.  and  height  of  the  center  pole  32 
ft.  ?    Ans.  :  id2.84-sq.  yds. 


MISCELLANEOUS.  73 

98.  The  diagonal  of  a  rectangular  field  containing  7J  acres  is 

50  rds.     Find  the  sides.     Ans.  :  30  and  40  rds. 

99.  Three  women  own  a  ball  of  yarn  10  in.  in  diameter.    Find 

what  each  will  wind  off  to  share  equally.  Ans.  :  ist, 
1.3-f-;  2d,  3.2-h;  and  3d,  5.5+10. 

100.  A  teacher  hired  on  conditions  if  he  had  40  pupils,  he  was 
to  get  $40  per  mo. ;  if  he  had  28,  he  was  to  get  $35  per 
mo.  It  so  happened  he  had  35  pupils.  What  should 
he  receive  ?     Ans.  :  $38.64x^5. 

loi.  How  much  water  will  a  bucket  hold  whose  upper  diame- 
ter is  13  in.,  its  lower  diameter  8^  in.  and  its  height  8J 
in.?    Ans.:  3  gal.  i  qt.  i— pt. 

102.  A  has  two  horses  and  a  cow.     The  first  horse  is  worth 

|6o.  The  first  horse  and  cow  together  are  worth  f  as 
much  as  the  second  horse,  and  the  second  horse  and 
cow  are  worth  twice  as  much  as  the  first  horse.  What 
is  the  value  of  each  ?     Ans.  :  Cow,  $40 ;  horse,  $80. 

103.  Ten  years  ago  I  was  \  as  old  as  my  father,  but  two  years 

hence  I  will  be  \  as  old.  What  are  our  ages  ?  Ans.  :  22 
and  46  yrs. 

104.  Two  men  engaged  to  build  a  barn  for  $540.     The  first 

worked  |  as  many  days  as  the  second,  plus  40,  and  re- 
ceived $300.  How  many  days  did  each  work  ?  Ans.  : 
ist,  ico;  2d,  80. 

105.  The  head  of  a  fish  weighs  one  pound,  the  tail  weighs  as 

much  as  the  head,  plus  \  the  body,  and  the  body  weighs 
twice  as  much  as  the  head  and  tail  both.  What  is  the 
weight  of  the  fish?     Ans.  :  12  lbs. 

106.  A  pole  134.  ft.  long  stands  on  a  bluff;  16  times  the  length 

in  the  ground  plus  6  feet  equals  \  of  the  length  in  the 
air  increased  by  80  ft.  How  much  is  in  the  air  ?  Ans.  : 
130  ft. 

107.  A  pile  of  wheat  in    the   corner  of  a  rectangular   room 

forms  a  portion  of  a  cone ;  the  pile  is  6  ft.  high  and  it 
is  5  ft.  from  edge  of  the  pile  to  corner  of  the  room. 
What  is  the  wheat  worth  at  $1  per  bu.  ?    Ans.  :  $31.55+. 

108.  The  amount  of  my  money  for  6  yrs.  at  6%  is  $300  more 

tha;;  the  amount  of  it  for  3  yrs.  at  10^,  How  mu^l? 
^^yel?    Ans.:  |5,ooo,  ,    .     —     . 


74  MISCELLANEOUS. 

109.  A  debt  with  interest  at  6%  was  paid  Aug.  18,  1893;  if  it 
had  been  paid  May  12, 1895,  there  would  have  been  due 
$26  more.     What  was  the  debt  at  first  ?     Ans.  :  $250. 

no.  The  3d  term  of  a  geometric  series  is  507  ;  the  first  term 
3.     Find  the  ratio.     Ans  :  13. 

111.  It  is  2  mins.  after  2  o'clock  p.  m.,  2^  30^^  east  long.     What 

is  the  time  31°  27'  30^^  west  long.  ?    Ans.  :  56  min.  after 

II  A.  M. 

112.  How  many  pens  must  I  buy  for  $1  so  that  I  may  gain 

20%  by  selling  them  4  for  i  cent?    Ans.  :  480. 

113.  The  present  worth   of  a  debt  at  6%  is  $660,  which   is 

$213.40  less  than  the  debt.  How  long  before  the  debt 
is  due  ?     Ans.  :  5  yrs.  4  mos.  20  days. 

114.  At  what  time  between  5  and  6  o'clock  is  the  min.  liand 

14  mins.  behind  the  hour  hand?    Ans.  :  12  mins.  after  5. 

115.  What  number  is  that  whose  square  is  22|%  of  the  cube 

of  8?    Ans.:  io|. 

116.  I  saved  $7.25  interest  by  paying  off  a  note  20  days  before 

due.     Find  the  face,  int.  6^.     Ans.  :  $2,000. 

117.  At  his  marriage  B  agrees  that  if,  at  his  death,  he  leaves 

only  a  daughter,  his  wife  shall  have  \  of  his  mone}-, 
and  if  he  should  leave  only  a  son,  she  should  have  \  ; 
he  left  a  son  and  daughter.  What  did  each  one  receive 
if  he  left  $6,591?  Ans.:  Son,  $4563;  widow,  $1,521; 
daughter,  $507. 

118.  What  is  the  greatest  number  that  will  divide  27,  48,  90, 

and  174,  and  leave  the  same  remainder?    Ans.  :  21. 

119.  A,  B  and  C  pasture  an  equal  number  of  horses  on  a  field, 

of  which  A  owns  9  acres,  and  B  15  acres  ;  if  C  pays  $24 
for  his  pasturage,  how  much  should  A  and  B  receive? 
Ans.:  a,  $3;  B,  $21. 

120.  A,  in  buying  coffee,  found,  if  he  paid  11  cts.  per  pound, 

he  would  lack  30  cts.  of  having  money  enough  to  pay 
for  it ;  he  bought  at  10^  cts.  and  had  15  cts.  left.  How 
many  pounds  did  he  buy  ?    Ans.  :  90  lbs. 

121.  A  bought  at  one  time  5  pears  and  6  peaches  for  28  ct3., 

and  at  another  time,  6  pears  and  3  peaches  for  21  cts. 
What  was  the  cost  of  each  kind  of  fruit  ?  Ans.  :  Pears, 
2  cts. ;  peaches,  3  cts. 


MISCELLANEOUS.  75 


122.  A  company  of  10  hire  a  team.     Two  fail  to  come  but  four 

others  join  the  company,  thus  reducing  the  estimated 
expense  to  each  by  50  cents.  What  does  each  pay  and 
what  does  the  team  cost?    Ans.  :  $1.25  and  $15. 

123.  If  40  cats  kill  40  rats  in  40  mins.,  how  many  cats  can  kill 

10  rats  in  10  mins.  ?    Ans.  :  40. 

124.  The  ages  of  A,  B  and  C  are  to  each  other  as  3,  4  and  5, 

and  their  sum  is  136  yrs.  What  is  the  age  of  each? 
Ans.  :  a,  34  ;  B,  45  J  ;  C,  56! . 

125.  A  and  B  were  partners  ;  A  put  in  $4,500  and  received  |  of 

the  profits.    What  was  B's  capital  ?    Ans.  :  $3,000. 

126.  What  number  multiplied  by  y\  of  itself  will  give  1,188? 

Ans.:  66. 

127.  A  teacher  hired  on  condition  that  if  he  had  20  pupils  he 

was  to  receive  $20  per  mo.,  and  if  he  had  12  pupils  he 
was  to  receive  $15  per  mo. ;  but  he  had  17  pupils.  What 
should  he  receive  ?    Ans.  :  $18.59!. 

128.  A  piece  of  cheese  weighs  4  lbs.  in  one  side  of  a  pair  of 

scales  and  9  lbs.  on  the  other  side.  What  is  the  true 
weight  of  the  cheese  ?    Ans.  :  6  lbs. 

129.  The  interest  on  \  of  A's  plus  f  of  B's  money  for  a  certain 

time,  at  2%,  was  to  this  sum  as  9: 250,  and  this  interest 
for  25  times  as  long,  at  10  times  as  great  a  %  was  $180. 
What  was  their  money,  if  A's  money  was  to  B's  as  1:3? 
Ans.  :  A,  $200  ;  B,  $600. 

130.  What  is  the  diameter  of  the  largest  circle  that  can  be  in- 

scribed in  an  equilateral  triangle  whose  sides  are  15  ? 
Ans.:  8.6+. 

131.  If  the  hands  of  a  clock  were  3  and  4  ins.  long,  how  far 

apart  would  the  points  be  at  3  o'clock  ?    Ans.  :  5  ins. 

132.  Find  the  side  of  a  square  lot  equal  in  area  to  a  circular 

one  60  rds.  in  diameter.    Ans.  :  53.1-i-rds. 

133.  What  is  the  diameter  of  a  round  field  of  such  size  that 

every  6  ft.  of  fence  is  equal  to  \  acre  ?    Ans.  :  7,260  ft. 

134.  The  area  of  an  equilateral  triangle  is  173.2  ft.    What  are 

the  sides?    Ans.:  i8.6i+ft. 

135.  The  axes  of  an  ellipse  are  as  2 : 3  and  its  area  is  125  sq. 

ft.    Find  the  diameters.     Ans.  :  10  and  15  ft. 


MISCELLANEOUS. 


136.  The   strength  of  two  men  are  as  3:4;   where  must  a 

weight  be  placed  on  a  spike  3^  ft.  long,  so  that  they 
may  carry  in  proportion  to  their  strength  ?  Ans.  :  \\ 
ft.  from  stronger  man. 

137.  A  newsboy  buys  papers  at  20  cts.  per  dozen,  and  sells 

them  at  a  nickel  apiece.  Find  his  per  cent,  of  profit. 
Ans.  :  200%. 

138.  What  %  of  .005  is  $100?    Ans.  :  2,000,000%. 

139.  A  and  B's  hotel  bill  was  $3 ;  A  pays  \  more  than  B.    What 

did  each  pay  ?    Ans.  :  A,  $1  f  ;  B,  $if. 

140.  A  board  is  18  ft.  long,  18  inches  wide  at  one  end  and  6 

ins.  at  the  other.  How  far  from  the  larger  end  must  I 
cut  it  across  to  divide  it  equally  ?    Ans.  :  6.5-l-ft. 

141.  How  much  lumber  in  a  board  12  ft.  long  and  one  inch 

thick  by  12  ins.  wide  at  one  end  and  2  ins.  square  at 
the  other  ?    Ans.  :  9I  ft. 

142.  How  many  posts  7  ft.  apart  will  it  take  to  fence  a  lot 

containing  70,756  sq.  ft.,  the  length  of  the  fence  being 
4  times  the  width  ?    Ans.:  190. 

143.  What  is  the  mean  proportional  of  9  and  16  ?    Ans.  :  12. 

144.  Find  the  side  of  the  largest  square  that  can  be  inscribed 

in  a  right  angled  triangle  whose  base  is  16  ft.  and  per- 
pendicular 12  ft.    Ans.  :  6.8+ft. 

145.  What  is  the  diameter  of  the  largest  cylinder  that  can  be 

cut  out  of  a  globe  30  ft.  in  diameter  ?    Ans.  :  24.5-f-ft. 

146.  What  is  the  solidity  of  a  cubical  box  that  will  hold  625 

lbs.  of  water  ?     Ans.  :  10  cu.  ft. 

147.  What  is  the  diameter  of  the  largest  circle  that  can  be 

inscribed  in  a  right  angled  triangle  whose  base  is  8 
and  perpendicular  6  ft.  ?    Ans.  :  4  ft. 

148.  f  of  A's  money  added  to  f  of  B's,  which  is  3  times  |  of 

C's,  being  put  on  interest  for  8  yrs.  at  5%  gives  $i8oo 
interest.  How  much  money  have  they  all  ?  Ans.  : 
$2,000. 

149.  A  building  whose  height  is  18  ft.  to  the  square  is  25  ft. 

wide,  and  the  rafters  on  one  side  are  15  ft.  and  on  the 
other  20  ft.  What  is  the  height  of  the  house  ?  Ans.  : 
30  ft. 


MISCELLANEOUS.  77 

i;o.  A  piece  of  ground  whose  3  sides  are  equal  cost  $375  at 
the  rate  of  $75  per  acre.  How  many  rods  of  fence  are 
required  to  inclose  it  ?    Ans.  :  120  rods. 

151.  What  time  between  5  and  6  o'clock  will  the  hour  hand  be 

midway  between  the  minute  hand  and  the  figure  5? 
Ans.  :  Half  past  5. 

152.  How  many  acres  in  a  rectangular  field  whose  sides  are  as 

2  to  3,  if  the  number  of  acres  in  the  field  _just  equals 
the  number  of  panels  in  the  fence  inclosing  it,  the 
panels  being  10  ft.  long  ?    Ans.  :  7,260. 

153.  I  find  my  watch,  which  keeps  correct  time,  is  3  hrs.  slow. 

How  far  and  in  what  direction  did  I  travel  ?  Ans.  : 
East  45°. 

154.  A  street  200  feet  wide  has  a  wall  on  one  side  100  ft.  high 

and  80  ft.  high  on  the  other  side ;  find  the  length  of 
the  shortest  line  that  will  reach  from  the  top  of  one 
wall  down  to  the  middle  of  the  street  and  then  to  the 
top  of  the  other  wall.    Ans.  :  269-f-ft. 

155-  $i)4oo  is  left  to  two  children,  whose  ages  are  11  and  16.  I 
want  to  invest  it  at  10%  so  that  each  will  have  the  same 
when  he  is  of  age.  How  shall  I  divide  it  ?  Ans.  :  $600 
and  $800. 

156.  A  rectangular  field  contains  lof  acres  and  the  sum  of  its 

sides  is  168  rds.     Find  the  sides.     Ans.  :  36  and  48  rds. 

157.  Awheel  4  ft.  in  diameter  stands  one  ft.  in  water ;  what 

fraction  of  the  wheel  is  in  the  water  ?    Ans.  :  .195-I-. 

158.  If  a  man  can  plant  a  field  100  rds.  in  diameter  in  4  days, 

how  long  will  it  take  him  to  plant  one  200  rds.  in 
diameter .?    Ans.  :  16  da. 

159.  Two  wheels,  one  6  ft.  in  diameter  and  the  other  4  ft.,  are 

on  an  axle  12  ft.  long,  and  are  started  to  roll.  How 
large  a  circle  will  they  inclose  .?    Ans.  :  72  ft.  diameter. 

160.  Find  the  diameter  of  the  3  largest  circles  that  can  be  in- 

scribed in  a  circle  whose  circumference  is  128  ft. 
Ans.:  i8+ft. 

16  r.  A  lot  lies  between  two  parallel  roads  \  mile  apart ;  it  is 
90  rds.  on  one  road  and  75  rds.  on  the  other.  What  is 
the  lot  worth  at  $80  an  acre  .?    Ans.  :  $6,600. 


78  MISCELLANEOUS. 

162.  I  have  a  circular  piece  of  land  5  rds.  in  diameter,  from 

which  I  take  enough  earth  to  fill  a  cone  whose  base  is 
10  ft.  in  diameter  and  15  ft.  deep.  How  much  was  the 
lot  lowered  ?    Ans.  :  .o734H-ft. 

163.  Find  the  solidity  of  an  octahedron  whose  linear  side  is  6 

in.    Ans.  :  ioi.82-|-cu.  in. 

164.  What   debt  can  be  discharged  in   12  days  by  daily  pay- 

ments which  are  in  geometrical  progression,  the  sec- 
ond payment  being  3  cents  and  ratio  being  8?  Ans.: 
$36,814,005.39. 

165.  The  length  of  the  hypotenuse  is  10  ft,  the  sum  of  the 

base  and  altitude  14  ft.  What  is  the  base  and  altitude  ? 
Ans.  :  Base,  6  ft. ;  alt.,  8  ft. 

166.  How  much  will  I  make  by  borrowing  money  at  5%  to 

pay  a  debt  of  $6,400,  due  in  8  mos.,  allowing  the  pres- 
ent worth  of  this  debt  to  be  reckoned  by  deducting 
5%  per  annum  discount?    Ans.  :  $7.11+. 

167.  B  wishes  to  divide  $290  between  his  two  sons  A  and  D, 

whose  ages  are  respectively  15  and  19  yrs.,  in  such  a 
manner  that  the  parts  bearing  simple  interest  at  \o% 
shall  amount  to  such  sums,  when  they  are  21  yrs.  of 
age,  that  f  of  A's  money  shall  be  equal  to  f  of  D's. 
Ans.  :  A's,  $90 ;  D's,  $200. 

168.  B  owns  a  piece  of  land  320  rds.  long  and  180  rds.  wide, 

and  wishes  to  lay  it  off  into  the  smallest  practicable 
number  of  square  fields.  What  will  be  the  number  of 
fields  and  what  is  their  size  ?  Ans.  :  144  fields  20  rds. 
square. 

169.  How  far  will  a  heavy  ball   fall   in   20  seconds  ?    Ans.  : 

6,400  ft. 

170.  What  is  the  diameter  of  each  of  the  four  largest  circles 

that  can  be  inscribed  in  a  larger  circle  whose  radius  is 
10  ft.?    Ans.:  4.14-l-ft. 

171.  A  body  falls  904^^  ft.  in  7^  seconds.     How  far  does  it  fall 

the  first  second  ?    Ans.  :  i6yV  ft. 

172.  Find  the  difference  between  two  numbers  whose  sum  is 

12  and  their  product  35  ?    Ans.  :  2. 

173.  The  sum  of  two  numbers  is  16  and  their  difference  is  2. 

Find  the  numbers.     Ans.  :  7  and  9. 


MISCELLANEOUS.  79 

174.  The  diflference  between  two  numbers  is  3,  and  their  prod- 

uct 180.     What  2re  the  numbers?    Ans.  :  12  and  15. 

175.  The  sum  of  two  numbers  is  7  and  the  sum  of  their  cubes 

133.     Find  the  numbers.     Ans.  :  2  and  5. 

176.  The  diameter  of  each  of  four  ec^ual  circles  that  can  be 

inscribed  in  a  larger  circle  is  4  ft.  What  is  the 
diameter  of  the  larger  circle  ?    Ans.  :  19.31-j-ft. 

177.  The  sum  of  the  squares  of  two  numbers  is  41  and  the 

difference  of  their  squares  9.  What  are  the  numbers? 
Ans.  :  4  and  5. 

178.  The  sum  of  two  numbers  is   19  and  the   sum  of  their 

squares  193.     Find  the  numbers.     Ans.  :  7  and  12. 

179.  The  difference  of  two  numbers  is  7  and  the  sum  of  their 

squares  65.     Find  the  numbers.     Ans.  :  8  and  r. 

180.  Suppose  there  be  a  round  pole  20  ft.  high  and  i  ft.  in 

diameter  and  a  vine  entwines  itself  around  it  just  12 
times  at  equal  distances  from  bottom  to  the  top.  What 
is  the  length  of  the  vine?     Ans.:  42.79-f-ft. 

181.  A  boy  hired  on  conditions  for  12  weeks,  that  he  should 

receive  $12  and  a  coat.  At  the  end  of  7  weeks  the  part- 
ies separated,  and  it  was  found  that  the  boy  was  en- 
titled to  $5  and  the  coat.  What  was  the  value  of  the 
coat?     Ans.:  $4.80. 

182.  A  globe  6  in.  in  diameter  weighs  25  lbs.     What  is  the 

weight  of  another  of  like  metal  3  in.  in  diameter? 
Ans.:  3.12-l-lbs. 

183.  The  sides  of  two  square  pieces  of  ground  are  as  3  to  5, 

and  the  sum  of  their  areas  is  30,600  square  feet.  What 
is  the  side  of  each  piece  ?     Ans.  :  90  and  150  ft. 

184.  B  gives  $1,200  to  C  to  be  invested  in  trade  for  one  year, 

on  condition  that  if  C  add  $500  to  it  and  act  as  mana- 
ger he  shall  have  |  of  the  gain.  What  was  C's  time 
worth?     Ans.:  $300. 

185.  A  has  4  sons,  whose  ages  differ  from  each  other  4  yrs. 

and  the  youngest  is  half  as  old  as  the  oldest.  Find 
the  age  of  each.     Ans.:  12,  16,  20  and  24  yrs. 


8o  MISCELLANEOUS. 


i86.  A  and  B  together  have  60  sheep,  and  if  you  divide  what 
A  has  by  what  B  has  the  quotient  will  be  3.  Required 
the  number  each  has.     Ans.  :  A,  45 ;  B,  15. 

187.  A  owns  720,  B  336  and  C  1,736  rods  of  land.     They  agree 

to  divide  it  into  equal  lots,  fixing  on  the  greatest  num- 
ber of  rods  for  a  lot  that  will  allow  each  owner  to  lay 
out  all  his  land.  How  many  sq.  rods  must  there  be  in 
a  lot  ?    Ans.  :  64. 

188.  It  is  required  to  find  a  sum  of  money  of  which,  in  the 

space  of  4  yrs.,  the  true  discount  at  simple  interest  is 
$5  more  at  the  rate  of  6%  than  at  4%  per  annum. 
Ans.:  $89.90. 

189.  If  a  railroad  carry  4,500  pounds  1,800  miles  for  $27,  how 

far  can  3,000  pounds  be  carried  for  $11  ?    Ans.  :  1,100  mi. 

190.  An  equilateral  triangle  whose  sides  are  8  is  inscribed  in 

a  circle.  What  is  the  circumference  of  the  circle  ? 
Ans.:  2S.99-J-. 

191.  How  many  acres  in  a  field  in  the  shape  of  a  parallelogram 

whose  diagonal  is  100  rods  and  the  difference  of  the 
squares  of  the  sides  is  2,800  ?    Ans.  :  30  acres. 

192.  The  difference  in  the  sides  of  a  grass  plot  is  9,  and  of 

their  squares  135.     Find  the  sides.     Ans.  :  12  and  3. 

193.  The  diameter  of  3  equal  circles  touching  each  other  is  10 

ft.    What  is  the  inclosed  space  ?    Ans.  :  4.034-sq.  ft. 

194.  The  altitude  of  a  field  in  the  shape  of  an  equilateral  tri- 

angle is  60  rds.  What  will  it  cost  to  fence  the  field  at 
80  cts.  per  rod.?     Ans.:  $i66.i7-f-. 

195.  How  many  acres  in  a  square  field  whose  diagonal  is  24 

rods  longer  than  its  side  ?    Ans.  :  20.9-I-. 

196.  The  area  of  a  parallelogram  is  140  square  rods.,  and  it  is 

inclosed  with  48  rods  of  fence.  What  are  its  dimen- 
sions ?     Ans.  :   14  and  10  rds. 

197.  A  garden  is  4  rods  longer  than  it  is  wide  and  contains 

140  square  rods  of  ground.  What  are  its  dimensions  ? 
Ans.:   14  and  10  rds. 

198.  A  parallelog^ram  is  6  rods  longer  than  it  is  wide,  and  its 

diacjonal  is  30  rds,  Hqw  many  rods  d-oes  it  contain? 
Ans.:  432  rds, 


MISCELLANEOUS.  8i 


199.  A  gentleman  told  a  lady  that  his  age  was  25,  intimating 

that  he  would  be  glad  to  know  how  much  he  was  her 
senior.  The  lady  replied :  "  The  square  root  of  the 
product  of  yours  by  mine  is  equal  to  4  times  the  square 
root  of  your  own."  What  was  the  age  of  the  lady? 
Ans.  :  16. 

200.  Says  Charlotte  to  her  brother,  Mr.  S.  has  lived  as  long  as 

both  Jane  and  I  together,  and  if  his  age  be  multiplied 
by  mine  the  product  would  be  420;  but  if  my  age  and 
hers  be  multiplied  the  product  is  only  224.  What  are 
the  ages  of  the  young  ladies?  Ans.:  Charlotte,  14; 
Jane,  16. 

201.  Three  men  are  to  carry  a  stick  of  timber  of  iiniform  size 

10  ft.  long,  two  at  the  spike  and  one  at  the  end  of  the 
stick.  How  far  from  the  center  of  the  stick  must  the 
spike  be  placed  so  that  each  may  carry  equal  weight  ? 
Ans.  :  2J  ft. 

202.  What  is  the  diameter  of  each  of  7  the  largest  circles  that 

can  be  inscribed  in  a  larger  one  15  ft.  in  diameter  ? 
Ans.  :  5  ft. 

203.  A  stick  of  timber  20  ft.  long  and  of  uniform  size  is  to  be 

carried  by  4  men  and  one  boy,  the  boy  equal  to  ^  of  a 
man,  the  men  at  the  spike  and  the  boy  at  the  end. 
How  far  from  the  center  of  the  stick  must  the  spike 
be  placed  ?     Ans.  :  i  J^  ft. 

204.  If  a  board  18  in.  wide  at  one  end  and  6  in.  wide  at  the 

other  and  12  ft.  long  be  divided  into  3  equal  pieces, 
how  far  from  the  wide  end  must  each  division  be  made  ? 
Ans.:  2.6  and  5,7  ft. 

205.  A  ball  10  in.  in  diameter  is  put  into  a  cubical  box,  each 

side  of  which  is  10  in.  What  will  be  the  diameter  of 
each  of  the  four  largest  balls  that  can  be  placed  in  the 
four  corners  ?    Ans.  :  2.68-f-in. 

206.  How  many  feet  of  lumber  in  a  stick  of  timber  2  x  4  ft.  at 

one  end  and  i  x  6  at  the  other,  and  12  ft.  long  ?  Ans.  :  80. 

207.  A  piece  of  land  is  17  rds.  wide  at  one  end  and  7  rds.  at 

the  other  and  60  rds.  long.  How  far  from  the  larger 
end  must  it  be  cut  straight  across  so  that  the  area  of 
the  two  parts  shall  be  equal  ?    An^.  :  24  Td3, 


82  MISCELLANEOUS. 


208.  A  stick  of  timber  of  uniform  size  and  20  ft.  long  is  to  be 

carried  by  one  man  and  4  boys,  the  boys'  strength  each 
being  equal  to  |  of  a  man.  How  far  from  the  center 
must  a  spike  be  placed  so  that  each  may  carry  the 
same,  the  man  being  at  the  end  and  the  boys  at  the 
spike  ?    Ans.  :  3^  ft, 

209.  What  is  the  diameter  of  each  of  the  four  largest  circles 

that  can  be  inscribed  in  an  equilateral  triangle  whose 
sides  are  24  inches  ?    Ans.  :  6.9-l-ft. 

210.  What   will    10  yds.  of  cloth  cost  at  liG-^f^-  per  yard? 

Ans.  :  $10,001. 

211.  If  a  man  weigh  300  lbs.  on  the  earth,  what  will  he  weigh 

on  the  moon  ?    Ans.  :  50  lbs. 

212.  The  hypotenuse  is  74  ft.  and  the  base  and  perpendicular 

are  equal.     How  long  is  the  base  ?    Ans.  :  52.34-ft. 

213.  What  number  divided  by  6,  7,  8,  9,  10  and  12  will  always 

leave  5  for  a  remainder?    Ans.  :  2,525. 

214.  The  sides  of  a  field  are  as  3  : 4  and  diagonal  60  rds.    What 

are  the  sides  ?     Ans.  :  36  and  48  rds. 

215.  The  area  of  a  garden  is  3  acres  and  its  boundary  104  rds. 

What  are  the  sides  ?    Ans.  :  40  and  1 2  rds. 

216.  If  a  log  2  ft.  in  diameter  will  make  300  ft.  of  lumber, 

what  will  one  of  the  same  length  and  4  ft.  in  diameter 
make  ?    Ans.  :  1,200  ft. 

217.  A  stone  fell  into  a  cistern  10  ft.  in  diameter  and  the  wa- 

ter in  the  cistern  rose  6  in.  What  is  the  content  of 
the  stone  ?    Ans.  :  39.27  cu.  ft. 

218.  The  solidity  of  a  cone  is  56  cu.  ft.,  and  the  diameter  of 

the  base  3  ft.  Find  the  altitude  of  the  cone.  Ans.: 
23.764-ft. 

219.  Find   the   solidity  of   a  prolate   spheroid  whose  polar 

diameter  is  20  and  equatorial  diameter  15  ft.  Ans.: 
2,8o6-j-cu.  ft.  approximately. 

220.  How  many  acres  in  an  equilateral  triangular  field  of  such 

size  that  the  number  of  acres  in  the  field  will  equal 
the  number  of  panels  in  the  fence  surrounding  it,  the 
panels  being  straight  and  12  ft.  long?    Ans.:  7,071-!- 


MISCELLANEOUS.  83 

221.  A,  B  and  C  live  at  the  corners  of  a  triangular  field;  from 

A  to  B  is  100  rds. ;  from  B  to  C  80  rds.,  and  from  C  to  A 
120  rds.  They  want  to  dig  a  well  that  shall  be  the 
same  distance  from  each.  How  far  from  each  to  the 
well?    Ans.  :  60.52-f-rds. 

222.  What  is  the  side  of  the  largest  square  that  can  be  in- 

scribed in  an  equilateral  triangle  whose  sides  are  12 
in.?    Ans.:  5.564-in. 

223.  What  is  the  side  of  the  largest  square  that  can  be  in- 

scribed in  a  right  angle  triangle  whose  sides  are  6,  8 
and  10  in.  ?    Ans.  :  3|4-i^« 

224.  What  is  the  diameter  of  the  largest  circle  that  can  be  in- 

scribed in  a  right  angled  triangle  whose  sides  are  12, 
16  and  20?    Ans.:  8. 

225.  What  is  the  diameter  of  the  largest  circle  that  can  be  in- 

scribed in  an  isosceles  triangle  whose  base  is  9  ft.  and 
equal  sides  20  ft.  6  in.  ?    Axs. :  7.24-ft. 

226.  At  what  figure  must  Tennessee  5's  be  bought  to  give  the 

buyer  5|§%  on  his  investment?    Ans.:  92^. 

227.  What  is  the  area  of  the  largest  square  that  can  be  in- 

scribed in  a  semi-circle,  the  diameter  of  the  circle  be- 
ing 20  in.  ?    Ans.  :  80  sq.  in. 

228.  Two   similar  fields   together   contain   518   square  rods. 

What  is  the  area  of  each  if  their  like  sides  are  as  5  to 
7  ?    Ans.  :  175  and  343  sq.  rds. 

229.  A  wheel  on  a  locomotive  is  5  ft.  in  diameter,  and  a  fly 

rides  on  the  rim  of  the  wheel.  How  far  does  the  fly 
travel  while  the  locomotive  runs  10  miles  ?  Ans.  :  15.9 
-f-miles. 


FRACTIONS. 


FRACTIONS. 


(i)   To  cut  each  piece  once=50  cts. 

To  cut  each  piece  twice=$1.00,  Ans. 

(2)  i-i=jV;  ^V=l;  1^=20;  20=iof  less;  f =80  less. 
20—1=19 ;  19=1  of  larger  ;  |=95  larger,  Ans. 

(3)  |— f=i ;  i=28 ;  f =^252  larger,  |  of  252=224  smaller,  Ans. 

(4)  \-\=-h\  3rV=3;  If =60,  Ans. 

(5)  i+i==T\  ;  ^=15  ;  tV=3  ;  i|=54,  Ans. 

(6)  f=A;  f=B;  |  of  |=l.f  C  ;  f4-f+H=H. 

||=$770;  5V=$10;  ||=$450  A. 
I  of  $450=1180  B ;  I  of  $180=$140  C,  Ans. 

(7)  |=length;  f-f =J ;  |=6;  |=1 8  ft.  length. 
I  of  18=12  ft.  breadth,  Ans. 

(8)  1  time  A's— 120=^  B's ;  3  (A's— 120)  or«3A's— 360=B's ; 

also  C's=2  B's  or  2  (3A's— 360)=6A's— 720.  lA's-}-3 
A's— 360+6A's— 720=6450.  10  times  A's=6450-f360-f 
720=7530  A's=753;  B's=(753— 120)X3=1899.  1899x2 
=3798  C's,  Ans. 

(9)  J-J=^,  i=6;  1=36;  i=36;  |=180,  Ans. 

(10)  2  persons  receive  15c  each  and  one  9c  ;  3  persons  receive 

39c,  or  13c  average  price. 
$4.68-^1 3c=36,  Ans. 

(11)  f=$45;  ^=$63;  45+4J=49J;  49J-h63=}^,  Ans. 

(12)  1+1=1  B ;  12X|=21  da.  B ;  i=21 ;  f=28  da.  A,  Ans. 


FRAtriONS.  83      i 

i 


(13)  f=B;  f=f ;  -|=A;  t^^+«=M;  H=$5700. 

ia=$3000  B. 
-/^=$2700  A,  Ans. 

(14)  l=A;  i=|;  1=1;  |=B;  f  of  f =^ ;  ^=f;  |=V-; 
-i^=C;  f+f+i^=!l;  f^=$540;  i|=$240A. 
|=$160  B ;  x^2=$140  C,  Ans. 

(15)  T3        \f^\^\    T3       T3  =  r3  >    73=^1'^^^. J    T I  ^^l"'*^. 

$1444|-f$1000=$2444|,  Ans. 

(16)  i  :  I  as  2  :  3 ;  2+3=5  ;  f  of  490=196  smaller. 
f  of  490=294  larger,  Ans. 

(17)  \\A-h=\\\  If4-H=f!;  !!=1357;  H=649  smaller. 
12=708  larger,  Ans. 

(18)  1-1=1;  f=$36;  f=$48.    |+i=f; 
6=$48 ;  |=$40,  Ans. 

(19)  i+!=M;lf-^34=2H<la.,ANS. 

(20)  tV-?V=^V;  11-^2^=24  da.,  Ans. 

(21)  ,^—}=f  A;  J^  of  f=/o  ;  f+T%=M;  f|-5-l=T'Tr  of  D's,  Ans. 

(22)  1=1 ;  3=1-1 ;  I  of  12=1,  ANS. 

(23)  l=C;  1+1=1  B;  f  of  |=V^ ;  |+V=¥;  ¥-^!=2|.  Ans. 

(24)  1=1;  l=f;  f+f=¥;  |h-V=A,ans. 

(25)  i+i=2^o;  lg-/^=U;  M-/o=tV;  tV=8;  1§=80,  ans. 

(26)  I— f=i;  1=12;  1=30;  f  of  30=21  f  yrs. 
30— 21f=8f  yrs.,  Ans. 

(27)  fX4=f;  fX2=-V-;  ¥— l=V-;  -^-=100;  f=90,  Ans. 

(28)  if-A=TV ;  f  of  ,7^=,?, ;  T?^-A=iV ; 

^^^=$2100  ;  f  f=$10,800,  Ans. 

(29)  1+1=0^  ;  l=$21  ;  |=$15  cost  A. 

I— 1=1 ;  l=$15  ;  f=$25  cost  me,  Ans. 


86  FRACTIONS. 


(30)  |=B;  |+1=|=A;  1+1=1;  1=54;  |=24  A. 
1=30  B,  Ans. 

(31)  K?=f;  ?-f=?;  f=8ft.;  |=18|  ft,  Ans. 

(32)  t^t^-|=tV  ;  tV=6  ;  ie=60  B  ;  i  of  60=18  A,  AxNS. 

(33)  \-\=\  ;  $6+$9=$15  ;  i=$15  ;  |=$120  B.       . 
\  of  $I20=$105 ;  $105— $6=$99  A,  Ans. 

(34)  1=1;  1=11;  i§-H=TV;  ^=2;  if=30  B'sage. 
11=32  A's  age,  Ans. 

(35)  f  of  8=6f  hrs.,  Ans. 

(36)  10x5=50  days  for  1  man. 
50-i-12=4^  da.  for  12  men. 
6 — 4^=1  days  saved,  Ans. 

(37)  1—1=!;  !-|=i;  i=$900;  |=$4500,Ans. 

(38)  1+7=8,  the  worth  of  both. 
I  of  8=6-1 ;  6f-T-7=|f,  Ans. 

(39)  1=1;  1=1;  l+f=V-;  ¥=102;  |=48  smaller. 
1=54  larger,  Ans. 

(40)  i— J=l;  8+12=20;  1=20;  |=80,  Ans. 

(41)  8+4=$12;  $12-i-3=$4;  $4x8=$32,  Ans. 

(42)  fcxl2=9c;  10+9=19c  cost. 
icxl2=3c;  19+6=25c,  Ans. 

(43)  iVof  $1.00=10c;  2|-=-10=H,Ans. 

(44)  10-4-3=3^0  ;  3J— J=2fc  cost. 
10-T-4=2ic  ;  2f — 2^=Jc,  Ans. 

(45)  4  qt.=J  bu.;  I— J=J;  |=6  bu. ;  %=^  bu.,  Ans. 

(46)  1=30;  1=50;  i-f=|;  f =6 ;  1=15. 
iz—h-=^i:U\  iH-5-Tk=21f  da.,  Ans. 

(47)  f+i=| ;  1+1=1 ;  4816-4-1=1806  ; 

f  of  1806=1204  smaller  ;  4816—1204=3612  larger,  Ans. 


FRACTIONS.  87 


(48)  f+f+l=Y-;  i-¥=TV,  ans. 

(49)  6Vx30=|t;  ^oX3=j%;  M-hA=T¥o. 
il§-T¥(y=T¥o- ;  t¥o^TV=l'  ^a.;  30-17=13  da.,  Ans. 

{50)   tV+*=2¥;  ^\— i=2¥  ;  h  of  2\=4V  a  in  one  da. 

1 1   J      T)  .     1 1   5      C 

T2        58 16-^)    t        16 T8    ^• 

?V4-iV+A=¥^^;  f|-^/8=5J  da.,  Ans. 

(51)  ^  of  f=J^  ;  J,  of  f=TV  ;  tV+tV=A  ;  ff^/3=5f  da.,  Ans. 

(52)  tV-^V=3V  ;  1 2^3'o=30  da.,  Ans. 

(53)  i^^-h=h\  ;  A-4¥8=if  8  ;  in-^if  8=81f  da.,  Ans. 

(54)  A,  \  acres  in  1  da. ;  B,  f ;  C,  ^ 
f-4-f+i=if  acres  together  in  1  da. 
2^-5-ff=li  da.,  Ans. 

(55)  l+l=H;  !f-H=H;  34--h=30,  ans. 

(56)  2|=V-;  -¥-+!=¥;  ¥=76-  |=20A;  24=56  B,Ans. 

(57)  t+l+f=|f;  M=88;  11=42  A;  f  of  42=28  B. 
f  of  42=18  C,  Ans. 

(58)  |=C,i=B,^%=A;  f4-|+^=M;  U=$440; 

f  fi=$200  C  ;  I  of  $200=$150  B  ;  ?  of  $150=$90,  Ans. 

(59)  i4-?+i-=I ;  1=98 ;  i=14  C  ;  1=28  B  ;  f=5G  A,  Ans. 

(60)  I— 1=J;  \—\=^-o\  $7+$3=$10;  -i2,=$l0;  j §=$75,  Ans. 

(61)  91-4-7=13;  91x7=637-4-13=49 larger;  91— 49=42  smaller, 

Ans. 

(62)  \—h-='h  ;  il^x'3=15  da.,  Ans. 

(63)  4-T-6=| ;  A  does  f  while  B  does  f  ;  |=20;  |=30  da.,  Ans. 

(64)  f  of  \  of  |=i\ ;  |=$t'o ;  •l=$H- ;  i\XlH=$||,  Ans. 

(65)  |-i=l;  f  of^=i^;  1-1-1^=11;  11=18  24;  11=11.52,  Ans. 

(66)  $12|-f$5^=$18i;  $125|-$18i-=$107i- ;  i  of  ^107if=$35|  A. 
$3o|-f-$5^=$41i,  B  ;  $41i+$7i=$48^  C,  Ans. 


FRACTIONS. 


{67)   H?=-V-;  45+20=65;  -y=6o;  i=35,ANS. 

(68)  1— i=| ;  1=100  ;  1=40 ;  |=140.    40  and  140,  Ans. 

(69)  l+J+J=M;  if-i=H;  il=5i;  ii=36,ans. 

(70)  J=20  ;  |=80c  cost ;  94—80=14  ;  14-j-7=2c. 
94-7-2=47,  Ans. 

(71)  J+i+i=^;  ^==118;  H=$24,an8. 

(72)  9|-4|=5;  5^2=2J;  2|+4|=6i;  6^X4=27^; 
27J-r-2J=ll,  Ans. 

(73)  -,%  of  t\=iVii  ;  iV(y=$40,500  ;  ^^=$165,000  ;  f  of  f=f ; 
f  of  $165,000=$70,714f,  Ans. 

(74)  I :  !  : :  3  :  4=^  A,  if  B  ;  ^^  of  $1520=$720  A. 
jl  of  $lo20=$800  B,  Ans. 

(75)  l=B;  1=1;  1=1  A;  |4-f=V-;  V-=153;  |=72  B. 
1=81  A,  Ans. 

(76)  f=100;  1=140;  140+100=240; 
240-T-18=13| ;  one  mile  in  13J  min.,  Ans. 

(77)  f =20  ;  |=26| ;  \  of  26f=6| ;  f  of  6|=4  hrs.,  Ans. 

(78)  One  man  can  do  ■^\^  in  one  day. 

\  of  12=2|  da. ;  ^i^X  V=Tk  ;  ifax3=f  ^g. 
!n-^T^iy=300,  Ans. 

(79)  $2660xl|=$4560  ;  \  of  $4560=$2280. 
$2280-i-2f=$840 ;  $840-t-2=$420,  Ans. 

(80)  7,250-1,250=6000;  |+|=-V  ;  ^=6,000; 

§=3200  B ;  ^  of  3200=2800;  2800+1250=4050  A,  Ans. 

(81)  7862X7^=58,965  ;  ^  of  t=f  ;  |  of  58,965=39,310  ; 

\  of  i=TV  ;  i^ij  of  39310=3931 ;  39310—3931=35379,  Ans. 

(82)  12+12=24;  1=24;  1=96  in.,  Ans. 

(83)  \-\=-\  ;  §  of  (J+24)=|+16  ;  (i+24)-(f+16)=^+$8. 

848— $3=$  10;  i=$40;  |=$360,  Ans. 


FRACTIONS.  89 


(84)  f-|=J;  h-\=h\  3+2=5;  J,=5;  ii=60 ; 
I  of  60=40  ;  404-3=43  gal.  acid. 

I  of  G0=15;  15-f-2=17  gal.  acid,  Ans. 

(85)  ^+(1  X|^f)~(J-^iV)  +  {f  X|)=i  Ans. 

(86)  $68+$I=$69  ;  f=$69 ;  f=$161 ;  ^  of  $I61=$80.50 ; 
$80.50— $G9=$12.50,  Ans. 

(87)  1-1-24=1;  f=|-h$32;  f+|=V-;  $5 12-$32=$510 ; 
-y-=$510;  |=$240;  240+32=$272  B's. 

$542— $272=$270  A's,  Ans. 

(88)  1=1+8;  1=1+12;  148-12=136;  f+f=-V-. 
-V-=136;  1=64  A;  |=72;  72+12=84  B,  Ans. 

(89)  $1.0.^fj=$l01;  $101X10=$1010,  Ans. 

(90)  I :  f  : :  f  :  f  =|f ;  A  :  B  as  63  :  64 ;  |  of  63=42  ; 
%  of  64=48 ;  48+42=90  ;  M  of  180=84  ; 

1=84 ;  1=126  A;  f f  of  180=96  ;  3=96  ;  f=128  B,  Ans. 

(91)  f=C,  f=B,  i+$12=A  ;  $645— $12=$633. 
1+1+^=2  0;  ^-|=$G.33;  i|=$379.80  C. 

J  of  $379.80=$ 1 89.90  B ;  (J  of  $189.90) +$12=$75.30  A,  Ans. 

(92)  \=i  times;  f=16  times;  16+1=17;   $170^1 7=$10  pig; 
$10xl6=$160  horse,  Ans. 

(93)  J=3;  1=9;  6=9;  1=1J;  i  of  50=10 ;  10x1^=15,  Ans. 

(94)  $1.00.o-2^=$6;  $6X100=$600,  Ans. 

(95)  20+20=40;  ^=40  yrs. ;  |=S0  C  ;  80— 20=60  B,  Ans. 

(96)  10X2=20;  35— 20=15  yrs.,  Ans. 

(97)  ^ij=wliat  thev  both  do  in  oue  hr. 
f+f=I;  1=20;  1=3^;  t|-=-J,=35  hrs.  B. 
1=35  ;  |=46f  hrs.,  A,  Ans. 

(98)  |+J=|;  1-1=1;  1=20;  |=26|,  Ans. 

(99)  ^=1;  1=1;  f-!=l;  1=8;  |=40b. 

4=48  A,  Ans. 


90  FRACTIONS. 


(loo)   lf-A=^;  iof  (t\4-65)={H+iB  ;  (r\+65)-(H+J-B 
=(i^T+-¥-);  {i'i+¥)=(|-l0);-«^4-l0=H^;  f|=33,ANs. 

(loi)   |=5Vj  of  (/r+l35) ;  f=$33 ;  y\  of  $33=$6  spent,  Ans. 

(102)  fof  5^=v-;  ^of  ^^=3^^;  ^v=¥-;  fl=^F; 

i|i=99  fur. ;  99-i-8=12|  mi.,  Ans. 

(103)  f+l=l;  ^of  |=J;  iof  f=^;  JXJ=^;  i=4; 
|=$36 ;  f  of  $36=$24,  Ans. 

(104)  |-J=|A;  1+100=1;  |=$100,  Ans. 

(105)  1=7^  rds.;  |=10  rds. ;  12-10=2;  100H-r22=600,  Ans. 

(106)  tV+A=M;  M^2=tV_^;  A-iVd=rk. 
^|^==$3500;  if ^=$60,000,  Ans. 

(107)  10+14=24  years;  f— J=|;  |=24;  |=36  father's  age  10 

yrs.  ago;  36+10=46;  46—1-1=32;  32—2=30;  30-4-2= 
15;  15+2=17.     15  and  17  yrs.,  Ans. 

(108)  f=what  he  had  at  first. 

1+1=1;  f  of  (|-$i6)=,4-v-. 

(|-$16)-(M-V-)=/o— V-. 

T%+I=M;  M— ¥=so;  Y-+-V=H^. 

\%-=^^-\^\  i§=$52,  Ans. 

(109)  !+}=!;  f=$40;  1=32  men. 
32X.20=$6.40;  f=$').40;  -|=$8. 
$40— $8=$32;  $32-t-32=$1.00. 
$40-^$1.00=40  men,  Ans. 

(no)  |+f=|§;  f§-f!=jV.    $15-$13=$2. 
tV=I2;  fg=$80,ANS. 

(111)  f-J=J^;  6+10=16.  x\=16 ;  i|=240. 
f  of  240=96  A ;  J=80  B  ;  80+96=176. 
240—176=54  C,  Ans. 

(112)  2X4=8;  20—8=12;  J=12;  |=36,  A. 
\  of  36=12  ;  12+2=14  B.  Ans. 


FRACTIONS. 


(113) 

22+13=35;  K^-  of  35=55  A. 

tV  of  55=5;  5—2=3;  j=3;  |=21  B,  Ans. 

(:i4)    i=l'i;  1=42  sum. 

J=4;  1=8;  42—8=34;  34-7-2=17  smaller. 
42— 1 7=25  larger,  Ans. 

(115)    g=4;  §=36  ;  75-j-l^=50  ;  50—30=14  ;  11-^-2=7  the  small- 
er.    50-7=43,  the  larger,  Ans. 

(i:6)    i=16;  1=80  sum.     80x4=320. 
480—320=100 ;  1C0-t-4=40  diff. 
80-f  40=120;  120-j-2=60,  the  larger. 
80—40=40 ;  40-r-2=20,  the  smaller,  Ans. 

(117)   Sl.O.ofa— ^.O0.oo%¥=^l;  $1X4=$4  gain,  Ans. 

(r  iS)    Goes  one  mile  in  f  of  an  hr. 
Comes  one  mile  in  ^  of  an  hr. 
f+J=l;  7^-H=13^  mi,  Ans. 

(119)  f=larger;  f  of  (|-287)=^  of  (|+287); 
1=451  larger,  Ans. 

(120)  1—1=1 ;  \  of  1=2^ ;  |-^V=H  cost. 

Tff — T0=T%>     To    ^^    T0=lt7;     TIT — 2^7=1^^  5     J-nh — M=^f» 

Ans. 

(121)  i~v=2V;  ^Vof  io=3|. 

A=3i;  f 5=70  gal.,  Ans. 

(i22)    f=smaller;  12^  times  f=V-,  the  larger. 
|4-5jO=54__i2J,  number  to  be  divided. 
i=T¥8 ;  1=11  smaller. 
12J-tf=llf  i  larger,  Ans. 

(123)  f=watch;  1  (|_[48-5])=48-f. 
|=$30  watch ;  $48— $30=$18  chain,  Ans. 

(124)  J  of  $30=$10  gain  ;  $10-t-125=8c  S.  P. 
=1;  1=8;  f=ec  C.  P.,  Ans. 


92  PERCENTAGE. 

(125)  I  of  $l=.66f ;  i=.66| ;  1=^-;  | 

3  of  130-= Y- ;  -'V^tV  ;  H=$20.  ? 

$20X10=$200,  Ans.  j 

(126)  20X4=80  ;  804-20=100  yrs.  sum  of  all  their  ages. 
|4-^=y- .  .i_o=ioo ;  1=90  sum  of  A  and  C.  '< 
\  of  90=10  C ;  80—10=70  B,  Ans.  ; 

(127)  1=3;  f=12;  if  8=12,  one  will  equal  \\\  90x1^=135;       i 
\  of  135=671,  Ans.  '  I 


PBRCBNTAGB. 


(1)  f+i=!;  f=$84;  f=$70;  $100-$70=$30. 

$30-r-$70=42f%,ANS. 

(2)  $72— $6=$66,  cost  of  f ;  \=\  of  $66=$22. 
|=$88,  cost  of  lot.    $100— $88=$12. 
$12-j-$88=13tV%,  Ans. 

(3)  \  of  ^1U=$2;   $10— $2=$8   cost;    $12— $8=$4 ;   $4-t-$8= 

50%,  Ans. 

(4)  $440H-(100%+10%)=$100cost. 

25%  of  $400=$100;  $400— $100=$300,  Ans. 

(5)  125%=A;  125%-i-2=62i%B;  100%— 62i%=37^%; 
37^%  =$225;  100%  =$600,  Ans. 

(6)  $300-M25%=$240;  $300-^75%  =$400. 
$400-j-$240=$640  C.  P.;  $300x2=$600  S.  P. 
$640— $600=$40  loss;  $40-j-$640=6J%,  Ans. 

(7)  100%4.20%=]20%;  100%— 20%=80%;120%— 80%=40%; 
40%=$250;  100%=$625;  80%  =$500,  Ans. 


PERCENTAGE. 


(8)  '%-''\ ;  1=1  cost  of  1st ;  f =cost  of  2d. 
^h%  of  1=1;  f+f=-V-  S.  P.  of  1st. 

lox-  of  f=^«o ;  H-^u=f§  s.  p.  of  2d. 

Y.+  9  9^i_y..  -y^9^$597;  fS=4270;  -|=$240,  Ans. 

(9)  1=^,  1=1;  |-f=i  gain.    i=^6f%,ANS. 

(10)  ^=?;    |=V;  -V— 7=f;  f=42f%,ANS. 

(11)  f  of  $300=$450  ;  $450-^3SJ%=$1350. 
^=$1350;  f=$2700,  Ans. 

(12)  23^  oiZ'^^%^^%\  8J%=$3350.50;  100^=$40206,  Ans** 

(13)  J  of  i  of  G0=5;  75%  of  33|%=25%. 
25%  =5;  100%=20,  Ans. 

(14)  ^^%  of  -I  of  100==26t;  5%  of  10  times  25%=12J%. 
12J%=26|;  100%=213^,  Ans. 

(15)  8^f^  of  i==jVo ;  ^Vo=$80;  f§fi=$l882TV,  Ans. 

(16)  \  of  $3003=$1000;  $1000^-62^%  =$1600,  Ans. 

(17)  37^%  of  i  of  20%  of  480=9. 

i  of  I  of  50%  of  324=36 ;  36—9=27,  Ans. 

(18)  $21-^(100%— 12|%)=$24  cost;  $24xll2J%=$27,  Ans. 

(19)  100%=labor;  30D%=material. 
100^^+4%  =104%;  300%— 15%  =285%. 

28o  %  4-104  %  =389  % ;  389  %  =$2334 ;  400  %  =$2400,  Anx-. 

(20)  100%=labor;  300%=material;  400%=both. 

100% +4%  =104%;  5%  of  300%=15%;  300%— 15%  =285% ; 
28o%+104%=389%;  400%— 389%=11%. 
11%=:$36;  100%=$600;  300%  =$1800,  Ans. 

(21)  $141.90-^(100%— 12^%)=$161.25. 
$161.25-j-(100^-|-7i%)=$150,  Ans. 

(22)  75%— G0%=15%;  15%=$1.00;  100%=$6t. 
60%  of  $6f=$4,  Ans. 


9A  PERCENTAGE. 


(23)   50^  of  $425=$212.50.  j 

30%  of  $425=1127.50;  $425— $127.50=$297.50.  \ 

20%  of  $297.50=$59.50 ;  $297.50— $59.50=$238.  ' 

$238-$212=$25.50,  Ans.  \ 

{24)   30%  of  $60=$18;  $60— $18=$42;  16f%  of  $42=$7.  ' 

$42— $7=$35  cost ;  5%  of  $60=$3 ;  $60+$3=$63.  ' 

$63— $35=$28,  Ans.  \ 

(25)  Jof$725.16=$241.72;  $725.16— $241.72=$483.44.  j 
5%  of  $483.44=$24.17 ;  $483.44— $24.17=$459.27,  Ans. 

(26)  f=|;  1=1;  |-f=i;  *=12J%,  Ans. 

(27)  140%  :  160%  : :  36  in  :  W=41f  in.,  Ans. 

(28)  100%+40%=140%;   10%    of  140%=  14%;   140%— 145^=m 
126%;  20%  of  126%=.252;  126%— .252=1.008. 
1.008— 100%=.008;  .008^100=f%,  Ans. 

(29)  30c-i-150%=20c  price  of  mixture. 
40c— 20c=20c;  20c-t-40c=50%,Ans. 

(30)  20%=30%;  1%=1J%;  100%=150%. 
100%4-30%=]30%;  150%— 130%=20%,Ans. 

(31)  100%— 20%=80%;  1=80%;  f=106f%; 
106f  %— 100%=6|%,  Ans. 

(32)  66f%of  240=160;  100%— ll^%=88f%. 
88|%=160;  100%=180;  20%=180;  100%=900,  ANi;. 

(33)  t=!;  f=f;  |-|=i;  i=20^ioss. 

(34)  $300-=-120%=$250costof  1st 
$300-T-75%=$400  cost  of  2nd. 
$400+$250=$650  cost  of  both. 
$300X2=$600  S.  P.  of  both. 
$650— $600=$50  loss,  Ans. 

(35)  100%-40%=60%;  60%=$30;  100%=$50, 
50%  of  $50=$25;  $50-|-$25=4/6. 
$76— $30=$45,  Ans. 


PERCENTAGE.  95 

(36)  100^—37^^=62^;^;  G2J%=$60;  100%  =$96. 
$96-=-(100%+20%)=$80;  $96— $80=$16,  Ans. 

(37)  8^=15%;  1%=U%;  100f^=187|%;  100%+15%=115%; 
187|%— 115%=72^%,  Ans. 

(38)  5%=J^;  -|§-2^n=H;  50cXl33J=66tc. 
66ic^H=.70i?c.  Ans. 

(39)  100-j-.005=2,000,000j^,  Ans. 

(40)  ioo%4-io%=iiof,  crii;  io%=tV; 

tV-H=tV;  tV=20;  ii=220%. 
220%— 100^=120%,  Ans. 

(41)  §=l;  1=1;  f-l=J;  i=i2i%. 

(42)  100%— 20%=80%;  80%=f ;  |— f=l. 
iof  f=i;  i=15%;  1=60%. 
100%— 60%  =40%,  Ans. 

(43)  20%  of  $180=$36  ;  $180-f  $36=$216. 
100%— 10%  =90%;  $2I6-i-90%=$240,  Ans. 

(44)  12%— 10%=2%;  2%=$150;  1 00%  =$7500  C. 
60%  of  $7500=$4500  ;  $7500-|-$4500=$12000  B. 

.  17500+$!  2000=$19500;  100%— 35%=65%; 
65%=$19500;  100%=$30000;  35%  of  $30000=$  10500  A, 

Ans. 

(45)  100%— 10%=90%;  90%=$18;  100%=$20. 

$20— $12=$8  ;  $8-r-10=80c  ;  $12-t-80c=15  lbs.,  Ans. 

(46)  100%— 25%=75%;  100%+25%=125%;  125%— 75%=50%. 
50%-^75%=66|%,  Ans. 

(47)  20%  of  $4=.80;  $4-|-.80=$4.80 

100%— 20%  =80%;  80%  =$4.80;  100%=$6,  Ans. 

(48)  $12550— $400=$12 150;  125%+100%=225%. 
225%=$12150;  100 %  =$5400  B. 

125%  of  $5400=$6750  ;  $6750+$400=$7150  A,  ANS. 


96  PERCENTAGE. 


(49)  ■!4-|=l;  |=$810;  |=$450;  |=$360. 
$360-4-(100%+33J%)==$270  C.  P.  of  1st 
$4o0-r-(100%— lli%)=$506.25  C.  P.  of  2nd. 
$o06.25+$270=$776.25. 

$810— $776.25=$33.75,  Ans. 

(50)  74  X  5=370  lbs. ;  370  X  .45=$166.50. 

2%  of  $166.50=13.33 ;  $166.50— $3.33=$163.17  j 
$163.17  X12J%  =$20.12+,  Ans. 

(51)  80%— 25%=55%;  100%— 55%=45%; 
45%=66f%;  100fo=US^S%. 

100-f-66f  %=166f%;  16^fc—US^\fc=mffo,  Ans. 

(52)  100%-j-(100%— 25%)=133J%;   100%^(100%4-25%)=80% 
133J%+80%=213J%;  213^%— 200%=13J%  loss. 
13J%=$30;  100%  =$225  S.  P. 

$225x80%=$180  1st. 
$225-7-(100%— 25%)=$300  2nd,  Ans. 

(53)  6cXl50=$9.00;  $9x  110%  =$9.90  ; 
100%— 5%  =95%;  6cX95%=5.7c. 

5.7c  X 100  lbs.=$5.70;  $9.90— $5.70=$4.20  ; 
$4.20-^-50  lbs.=8f  c,  Ans. 

(54)  100%=cost;  ^of  100%=50%;  50%Xl25%=62J%; 
f  of  100%=40%;  40%X112^%=45%; 
50%4-40%=90%;  100%— 90%=10%; 

J  of  10%=5%;  62J%+45%-h5%=112J%; 
$1125-?-112^%=$1000,  Ans. 

(55)  100%— 15%=85%;  5%  of  85%  =.0425 
85%— .0425=.8075 

100%— 5%=95%;  15%of  95%=.1425       ^ 
95%— .1425—8075 
.8075— .8075=0,  Ans. 

(56)  30%of  $850=$255;  $S50— $255=$595. 

2i%.of  $595=$14.87^  ;  $595— $14.87J=$580.12^,  Ans. 


PERCENTAGE,  97 


(57)  40%=60%;  100%=150^;  100^+150%=250^. 
250%  =4655;  100^=1862;  150  %  =2793,  Ans. 

(58)  100%— 24^=76%;  76%=$760;  100 %  =$1000,  Ans. 

(59)  100%— 12^%=87^%;  $1.60x87^%  =$1.40. 
$1.40-T-(100%— 30%)=$2.00,  Ans. 

(60)  $72X125%=$90;  $90-f-(100%-10%)=$100,  Ans. 

(61)  $480 XI 12^%  =$540;  1^%=$540;  100%  =$36,000,  Ans. 

(62)  $120  -^  (100%  —  8%)  =  $130^f  ;  $130|f  X  (100%  — 10%)  = 

$1172%,  Ans. 

(63)  $105-f-(100%+25%)=$84. 

$10o-f-(100%— 2o%)=$140;  $140+$84=$224  C.  P. 
$105X2=$210;  $224— $210=$14  loss,  Ans. 

(64)  75%  of  $600=$450;  3J%=$450;  100%  =$1350. 
^=$1350 ;  |=$2700,  Ans. 

(65)  25%  of  i=jV;  tV=$350;  if =$4200,  Ans. 

(66)  100%— 20%=80%;  6%of  80%=.04;  80%— 4%=76%. 
(100%  4-15%)— 76%  =.39;  .39-5-76  %=51t'V%,  Ans. 

(67)  10%of  125%=12J%;  125%— 12J%=112^%. 

112^%- 100%=12i%;  12|%=$4684;  100%  =$37,472,  Ans. 

(68)  100%-Hl20%=83J%;  100%-r-125%=80%;   83J%  — 80%= 

3J%. 
3|  %  =$60 ;  100  %  =$1800 ;  $1800  X  83J  %  =$1500,  Ans. 

(69)  100%-^(100%  +  25%)=80%;  100%-=-(100%— 25%)=133J%. 
(133^%-f  80%)  — (100%X2)  =  13J%;   13J%=$60;   100%= 

$450. 
$450X80%  =$360  1st;  $450-t-75%=$600  2d,  Ans. 

(70)  $120X(100%— 25%)=$90;    $90xl33J%=$120;    $120— $120 

=0,  Ans. 

(71)  (100%+20%)  — (100%— 20%)=40%;  40%=$90;  100%= 

$225,  Ans. 


qS  percentage. 

(72)  J  of  $1200=$600 ;  $600xllo%=$690;  $90  gain. 
$600-4-1 5/=4000  yds.;  17^^X4000  yds.=$700;  $100  gain. 
$100-f-$90=$190,  Ans. 

(73)  |of  100^=60fc;  60%X130%=78%;  |of  100%=40%. 
40fcX{l00%—5fc)=SS%;  38%-f78%==116%;  116%— 100/^ 

=16% 
16  %  =$720 ;  100  %  =$4,500,  Ans. 

(74)  30%=x%'V;  T^^of  |=Agaiii. 

5%=Tf  (7  ;   T^TT  of  l=Tf^  loss. 

t5=t\\',  T\\—ih=j^j>  net  gain. 
in=l4500;  ji^=$4o;  ifo==$405,  Ans. 

(75)  $240X125%=$300;  $300-4-(100%— 2o%)=$400,  Ans. 

(76)  100%=rice;  160%=tea;  240%=coffee;  300%=sugar. 
100  %  +1 60  %  +240  %  +300  %  =800  % ;  800  %  =$240. 
100%=$30rice;  160%=$48tea;  240%=$72  coffee;  300% 

=$90  sugar,  Ans. 

(77)  ^of  100%=50%;  50%X120%=60%;  50%x90%=45%. 
(60%+45%)— 100%=5%;  $100^5%  =$2000,  Ans. 

(78)  100%-38%=62%;   25%  of  62%=  15|%;   62%+15|%  = 

100%— 77i%=22^%;  22J%=9A;  100%  =40  A,  Ans. 

(79)  i  of  100%=50%;  50%X120%=60%;  60%x(100%— 12i%) 

=43|%. 
60% +433%  =1031%;  103f%— 100%=3|%. 
3|%=$30;  1C0%=$800;  $800-j-300=$25,  ANS. 

(80)  100%-r-(100%+20%)=83J%;  K0%-^{100%— 20%)=125%. 
125  %  +83^  %  =208^  % ;  208  J  %  —200  %  =8^  % . 
8J%=$50;  100%=$600;  $G00x83J%=$500  Ist. 
$600-^80  %  =$750  2d,  Ans. 

(81)  100%— 10%  =  90%;  8<^xl30%=10.4<^j  10.4<?-^90%=11^)^ 
Ans. 


PERCENTAGE.  99 


(82)  $2.50X46=$115;  $115x125 ^=$143.75. 
46—6=40  gal. ;  $143.75-^40=$3.59|,  Ans. 


(84)  2|%=^V;H+3V=H,ans. 

(85)  10%  of  50^=5/' ;  50^4-5^=55^. 

25%  of  50^=12|c ;  55c4-12Jc=67K  Ans. 

(86)  10%  of  {100%4-33J%)=13J%;  133J%— 13J%=120%. 

120%— 100%=20%,  Ans. 

(87)  (100%+20%)-7-(100%-15%)=:141tV%. 
141xV%— 100%=41t\%,  Ans. 

(88)  I60Z.— 12oz.=4  oz. ;  4-7-16=25%,  Ans. 

(89)  $238-j-(100%— 20%)=$297.50  2d. 
$297.50H-(100%+40%)=$212.50  1st,  AnS. 

(90)  By  spending  50%  of  his  money  for  12  days  he  has  re- 

maining ToVi ;  tA¥=$i  ;  lMI=$i»024,  ans. 

(91)  $2,400-5-120%  =$2,000  gain  2d  yr, 

$2,000-r44|%  =$4,500  gain  1st  yr.,  AnS. 

(92)  268.8  cu.  in.— 231  cu.  in.=37.8  cu.  in. 

37.8  4  37.8  1 

=16— %  gain;  =14 — %  loss. 

231  11  268.8         16 

4  1  53 

16— %— 14— %=2 — %  gain,  Ans. 
11  16  176 

(93)  100%— (6%+30%)=64%;    40%  of  30%=12%;  30%— 12% 

=18%. 
64%4-18%=82%;    100%-hl4%=114%;  114%— 82%=32%. 
32  %  -7-64  %  =50  % ,  Ans. 

(94)  100%=C;  133J%=B;  133J%— 100%=33J%. 
33|%=$100  ;  100%  =$300  C;  4%  of  $300=$12,  AnS. 

(95)  100%— 25%=75%;  25%-^75%=33J%,  Ans. 


100  PERCENTAGE. 


(96)  100^+8^=108%;  108%X112J%=12H%. 

Vl\\%  X  (100%  —  4%)=116.64%  ;   $1,166.^0-^-116.64%  = 
$1,000,  Ans. 

(97)  100%— 18tV%=  81^9^%;  75%  of  (81x^i%+ $G5)=61/r%  + 
$48|. 
(8lT«T%+$65)-(61^x%+^8f)=20A/«+ll6l ;  $16J+$10= 

$26^. 
100%— 20i53.%=79x\%;  79T«r%=$26J;  100%  =$33,  Ans. 

(98)  100%=larger. 

75%  of  287=215i;  16§%  of  287=47|;  75%— 16f%=58J%. 
215i+47|=263jV ;  ^'^\%=1^2>^r^  100%=451,  Ans. 

(99)  6%=$15;  100%=$300;  $300h-$2.50=120,  Ans. 

(100)  $.193X10X100=$193,  cost. 

10%  of  100=10;  100—10=90  yds. 

$.238X10X90=$210.60  selling  price. 

$210.60— $193=$17.60  gain. 

$17.60-r-$193=9jV3%  gain,  Ans. 
(loi)   100%=B;  150%=A;  100%-T-150%=66f %,  Ans. 

(102)  40%  of  $100=$40;  $100+$40=$140  S.  P. 
100  %  —12^  %  =87^  %  of  asking  price. 
$140-T-87^%=$160,  Ans. 

(103)  \  of  100=40;  10%  of  40=4;  f  of  100=57f. 
4-5-57^=7%,  Ans. 

(104)  36  in.— 35  in.=l  in.;  1  in.-r-35=2f  %. 
40%+2f%=42f%;  42f%=$330;  100%  =$770,  Ans. 

(105)  100%4-12^%=112^%;  112^%— 90%=22^%. 
$18+$20=$38;  22^%=$38;  100%=$168|.  Ans. 

(106)  $24~-(100%— 25%)=$32cost;  $34— $32=$2. 
$2-^$32=6i%  gain,  Ans. 

(107)  100  %=eacli  investment. 
100%4-25%=125%  A;  ^  of  125%=62^%  B. 
I00%— 62J%=37*%;  37^%=$225;  100%  =$600,  Ans. 


INTEREST. 


(io8)  10%  of  120=12;  8+12=20;  5^=20;  100^=400,  Ans. 

(109)   $25-j-(100%— 16f %)=$30  1st. 

$30— $25=$5;  16%=$o;  100%=$31.25  2nd,  Ans. 

(no)    i%=$5;  100^=14000  cost. 

$6— $5=$1  gain ;  $l-r-$4000=5V%,  Ans. 

(111)  160H-140=lf  yds.,  Ans. 

(112)  $3h-150  <fo  =$2 ;  $4— $2=$2 ;  $2-r-$4=50  % ,  Ans. 

(113)  100%— 50%=50%;  6—1=5;  50-^-5=10%,  Ans. 

(114)  100%=costof  each;  100% +20%  =120%  rice;  100 fc +10 fc 

=110  fc  coffee. 
100%— 8%=92%;  120%+110%+92%=322%. 
322%  =$3,864;  100%  =$1,200,  Ans. 


INTEREST. 


(1)  $2,442.04X$1.61051=$3,932.9298  am't. 

The  sum  of  the  compound  am'ts  for  4,  3,  2, 1  and  0  yrs.s 

$6.1051. 
$3,932.9298-j-6.1051=$644.204,  Ans. 

(2)  365  da.-4-73=5 ;  $1.00+.10=$1.10;  v^no=1.924%,  Ans. 

(3)  f  mill=.24;  100%  =$1,080,  Ans. 

(4)  Am't  of  $1  at  12%  for  6  mo.=$1.0609;  $1.0609— 3>^  int.= 

$1.0309. 
Am't  of  $1.0309  at  12%  for  6  mo.— 3^=$1.06368181. 
Clearing  .06368181   on   each    $1;    $2,450.85 -r- .06368181= 

$38,485.87,  Ans. 


INTEREST. 


(5)  $750h-4=$187.50.     By  multiplying  $187.50  by  the  am't  of 

$1  at  simple  int.  for  4, 9, 12  and  20  mo.  we  have  $190,625, 
$194,531,  $196,875  and  $203,125,  which,  added  together 
make  $785,156,  Ans. 

(6)  4J%  of  $180  for  8  mo.=$5.40  ;  $1804-$5.40=$185.40. 
$185.40— $156=$29.40  gain  ;  $29.40-7-$156=18^i%,  Ans. 

(7)  The  am't  of  the  present  worths  of  $250  for  \,  \\,  2^,  Z\ 

and  4^,  and  the  remainder  in  5  yrs.  is  $3413.08+,  Ans. 

(8)  The  sum  of  the  present  worths  of  $200  for  1,  2,  3,  4  and  5 

mo.=$978.15,  Ans. 

(9)  Am't  of  $300  at  6%  for  1  yr.  10  mo.=$333. 

$1,500— $333=$1,167 ;  1  yr.  10  mo.=22  mo. ;  22—6=16  mo. 
Pres.  worth  of  $1,167  for  16  mo.  at  6%  =$1,080.56,  Ans. 

(10)  The  compound  am't  of  $1  for  1  yr .=$1.1 2550881. 
$1.12550881— $1=12.550881%,  Ans. 

(11)  '$100  at  2%  a  mo.  for  33  da.=$2.20 ;  $2.20xll=$24.20. 
$100+|24.20=$124.20 ;  $124.20— $106=$18.20,  Ans. 

(12)  $3,325  at  1%  for  10  mo.  24  da.=$29.925. 
$119.70-T-$29.925=4%,  Ans. 

(13)  1.00-T-6%=l6f  yrs.,  Ans. 

(14)  $6,000  at  1%  for  1  mo.=$5;  $45-4-$5=9%,  Ans. 

(15)  $1  at  1%  a  mo.  for  68  da.=.02x^j  ;  $17-r-.02T\=|750,  An& 

(16)  2.00-7-30  yrs.=6f  %,  Ans. 

(17)  100%— 40^=60%;  100%-T-60%=$lf. 
$lf  at  5%  semi-annually=16§%,  Ans. 

(18)  $4.00— $1.00=$3.00 ;  $3.00-4-24=1 2 J %,  Ans. 

(19)  Am't  of  $1  for  1  yr.  8  mo.  5  da.=$1.084yV 
$819.45-T-$1.0843V=$755.93,  Ans. 

(20)  $1.00-j-8=12J  yrs.,  Ans. 


INTEREST.  103 


(21)  24-3=5;  f  of  $2,640=11,584;  $l,584-r-2=$792  A's  int. 
$1  at  6%  for  5  yrs.  6  mo.=.33;  $792-r-.33=$2,400  A. 

f  of  $2,400=$1,600  B,  Ans. 

(22)  $1,480.78— $1,374.50=$106.28  int. 

106.28 

10%  of  $1,374.50=$137.45.     yr.=9  mo.  8  da.,  Ans. 

137.45 

(23)  6%  of  $175.12  for  1  yr.=$10.5072. 

6.43 

yr.=7  mo.  10  da.,  Ans. 

10.5072 

(24)  12%of  $3,642.08=$437.0496;  $4,007.54— $3,642.08=^365.46 ; 

365.46 

yr.=10  mo.  1  da.,  Ans. 

437.0496 

(25)  $100  at  2%  for  63  da.=$4.20;  $1004-$4.20=$104.20. 
.18235=int.  for  given  time;  $4.20-7-.18235=233i/3-%,  Ans. 

(26)  $1  at  6%  for  93  da.=.0155  ;  $1— .0155=.9845. 
$1,000-^.9845=$!, 015.74,  Ans. 

(27)  20%  of  $100  for  63  da.=$3.50;  $100-1-$3.50=$103.50. 

1%  of  $103.50  for  63  da.=.181125;  $3.50-j-181125=19jV7%» 
Ans. 

(28)  1%  of  $200  for  2  yrs.=$4;  $48h-$4=12%,  Ans. 

(29)  6%  of  $1  for  2  yrs.=.12 ;  $48h-.12=$400,  Ans. 

(30)  6%  of  $1  for  6  mo.  12  da.=.032;  $640-f-.032=$20,000. 
i=$20,000 ;  f=$100,000,  Ans. 

(31)  Compound  int.  of  $400  for  2  yrs.=$66.56. 
Annual  int.  of  $400  for  2  yrs.=$66.56. 
$66.56— $66.56=0,  Ans. 

(32)  Compound  int.  for  3  yrs.  at  6 %  =$38.20-1'. 
Annual  int.  for  3  yrs.  at  6%=$38.16, 
$38.20— $38.16=4^,  An§, 


104  INTEREST. 


(33)  Compound  am't  of  $200  at  8%  for  2  yrs.=$33.28. 
Simple  int.  of  $200  for  2  yrs.  at  8%  =$32.00. 
^3.28— $32=$  1.28,  Ans. 

(34)  37— 18=19  yrs. 

The  sum  of  the  compound  amounts  from  one  to  19  yrs. 
inclusive=$35.784-. 

$25,000-j-$35.78+=$698.74— ,  Ans. 

(35)  f  of  A's=|of  B's;  f=|;  |4-f=V-;  ^=$3,213. 

f =$1,512  B ;  f=$l,704  A's ;  8%  of  $1  for  3  yrs.  9  mo.=.30 ; 
|1,704^.30=$5,680  A's ;  $l,512-j-.30=$5,040  B's,  Ans. 

(36)  Am't  of  $1  for  2  yrs.  at  5%  =$1.10  ;  $4,950h-$1.10=$4,500. 
I  of  f=/:,;  |+A=ff ;  $4,500-4-ff=$4,375  farm. 

1=3?;  f=/r;  A  of  $4,375=$l,666f  house,  Ans. 
^37)   $1  at  8%  for  6  yrs.=.48  ;  $960-t-.48=$2,000. 
|-H=f;  $2,000 X|=$3,000B. 

\  of  $3,000=$1,500 ;  $l,500-r-3=$500 ;  §=$500 ;  |=$750  h , 

Aks. 

(38)  Amount  at  simple  int.  of  $1  for  6  yrs.  at  4%  =$1.24. 
$744-T-$1.21=$600. 

1+1=1;  1=1600;  |=$360A. 
f  of  $360=$240,  which  is  as  2  :  3. 
Then  §=$240 ;  |=$360,  Ans. 

.975 

(39)  $13X6%=.78;  =1  yr.  3  mo.,  Ans. 

.78 

(40)  2mo.=J^yr.;  i=$3.25;  f=$19.50;  $19.50-t-$325=6^, Ans. 

(41)  $68— $87=$1;  5%— 4%=1%;  $1.00-?-l%=$100  difference. 
$68+$67=$135;  5%+4%=9%;  $13o-r-9%  =$1,500  am't. 
$1,500— $100=$1, 400;  $l,400-r-2=$700 ;  $7004-$! 00=$800. 
$700  and  $800,  Ans. 

(42)  $1  at  5%  for  9  mo.=.0375  ;  $1  for  15  mo.  at  4%  =.05. 
.05— .0375=.0125;  $150-^.0125=$12,000,  Ans. 

(43)  $1.00-7-16  yrs.=6}f,,  Ans. 


INTEREST,  105 


(44)  $612— $558=$54 ;  4^  yrs.— 3  yrs.=lj  yrs. 
$54-j-l|  yrs.=$36  int.  for  one  year;  3  yrs.=$108. 
$558— $108=$450  prin.;  $36-r-$450=8%,  Ans. 

(45)  l=prin.;  f-!=f;  f=$120;  f =$200  prin. 
f  of  $200=$80,  Ans. 

{46)    5=prin.;  f-i=|;  |=$120 ;  f=$150,  Ans. 

(47)  |=int.  for  5  yrs. ;  \  of  f=i  int.  for  1  yr. ;  ^=12^%,  Ans. 

(48)  $LOO=prin.;  $1  at  3^%  for  8  yrs.=.28;  |of.28=.04;  .04-7- 
$1.00=2T>  Ans. 

(49)  For  1  yr.  it  is  yV  o  f  1=25 ;  2?=*% .  Ans. 

(50)  $1  at  11  %  for  9  yrs.=.99  ;  $l-h.99=$1.99 ;  $597-f-$1.99=|300. 
$363— $300=$363  ;  $300  at  11%  for  1  yr.=$33. 
$363h-$33=11  yrs.,  Ans. 

(51)  .23X365=$9.125;  $9.125-f-$l,460=6i%,  Ans. 

(52)  t  of  $723.16^  =  $451.978 J;  1\%  of  $723.16^  =  $54.2373| ; 
451.978J 

=8  yrs.  4  mo.,  Ans. 

54.23731 

(53)  $345— $790=$55 ;  19— 8=11  mo.;  $55-t-11=$5. 
$5X12=$60  int.  for  1  yr.;  $5x9=$45. 

$  45— $45=$800 ;  $60-j-$800=7^  % ,  Ans. 

(54)  ($139X600)— ($600xl39)=0,  Ans. 

(55)  ^i-f=f;  f=$640;  |=$560,  Ans. 

(56)  $4— $1=$3;  $3H-20yrs.=15%,  ANS* 


TOO  STOCKS  AND  BONDS. 


STOCKS  AND  BONDS. 


(1)  $100X32=$3200;  $3200X(100%— 15i%)=$2712,  Ans. 

(2)  18x$o00=$9000;  100^— 28%  =72^; 
102%—72fc=S0fc  loss;  $9000x30%  =$2700,  Ans. 

(3)  100%-4i%=95^%;  $4775^95^%  =$5000; 
$5000-r-$100=50,  Ans. 

(4)  6%^75%=8%;  100%4-8%=108%; 
$16200-M08%=$15000;  $16200— $15000=$1200; 
$1200X75%=$900,  Ans. 

(5)  6%-j-90%=6|%,ANS. 

(6)  7%=8%;  100%=ll4f%,ANS. 

(7)  8%=6%;  100^=75%,  Ans. 

S% 

(8)  $2000h =$32500.  Ans. 

130% 

(9)  $120x$10=$1200;  $1200x(f%4-U5&)=$23.  Ans. 

(10)  (100%4-2%)-i-(100%4-20%)=8o%;  1005&— 85%=155^.An& 

(11)  6%-r^7J%=16%,  A_N3. 

(12)  4%+5%=9%gain;  9%=$4o0;  100%=$o000; 
$o000-i-$50=100,  Ans. 

(13)  $6894-j-(95i%4-|%)=$7200,ANS. 

(14)  100%— 25%=75%  cost; 
100%+20%=120%  S.  P.;  120%— 75%=45%; 
45%-i-75%=60%,  Ans. 


STOCKS  AXD  BONDS.  107 

100%— 30^=70%. 

I  realize  4^+4%  or  8^  on  each  share  per  annum. 

8%-j-70%=llf%,ANS. 

(16)  $250x$100=$25000;  $25000x0%  =$1500; 
$2-5000x70%  =$17500;  $17500x(8%-T-120%)=$1166f ; 
$1500— $1166f=$333^,  Ans. 

(17)  A\%  of  $100=^.50;  $100— $4.50=$95.50; 
$4775-=-$95.50=50,  Ans. 

{18)   $100x50=$o000;  J%  of  $5000=$25. 
$2348.20-i-($5000— $25)=47i%,  Ans. 

(19)  6%-T-90%=6t%. 
15%-j-6§%=2,K 
100%x2i=225%,ANS. 

(20)  115%X8%=9.2%;  9.2%-^90%=10|^,  Ans. 

(21)  6%  of  $50=$3;  $3.00-7-8%  =$37.50,  Ans. 

(22)  $500X1H=$456.52^\,  Ans. 

(23)  8%=5%;  100%=62^%,  Ans. 

(24)  $3XI0-r-5«5=$35625,  Ans. 

(25)  (6%-r-107%)Xl50%=8^\%,  Ans. 

(26)  (6%-^104%)Xl2y%=7||%,  Ans. 

(27)  105%X8%=8.4%;  &%=&A%\  100%=140,Ans 

(28)  5%  of  $9500=^75. 
^75XJ^^=$273.125,  Ans. 

(29)  $8500X1 15%  =$9775,  Ans. 

(30)  $21300-T-106.5%  =$20000;  $20000x  109%  =$21800; 
$21800— $21300=$500,  Ans. 

(31)  $1.-T-105%  =$.95^=953^  cents,  AnSw 

(32)  $800X110J%=$881,  Ans. 


7o8  STOCKS  AND  BONDS. 

(33)  Int.  on  $1.  at  If  %  for  4  intervals=$.065-^  \ 
1513.50 -^$.065— =17900,  Ans. 

^% 

(34)  $1000-5 ^=$16153.84^,  Ans. 

105% 

(35)  100%4-4%=104%;  hfo  of  104%=5.2^. 
104%-f5.2%=109.2%. 
$12012-5-109.2  %  =$11,000. 
$ll,000-r-$100=110  shares,  Ans. 

r 

{36)    ($4982-^106 f^)X4%=$188,  Ans. 
(37)   7%-=-70=10%,Ans. 

(38)  {ioofc-m-imro+kfc)=Hfc; 

9i%=$925;  100%=$10,000; 
$lO,000-r-$100=100,  Ans. 

(39)   $1921^{Tf^xll3%)=$40120,  Ans. 

{40)  $100x25=$2500;  5%  of  $2500=$  125; 
$125-r-$2.50=50  per  yr. ;  10  nio.=|  yr. 
50-4-1=60  lamps,  Ans. 

(41)  25X$1000=$25000;  $25000X(114^%+J%)=$28593.75, AnS. 

(42)  $2d734.37^4-$15.62^=$25750 ; 

j\fc=$lo.(j2}^;  100%=$25000. 
$25750-r-$25000=103%,  Ans. 

(43)  $3220;.VTiiiXl05%)=$283.50,  Ans. 

(44)  r25x$100=$12500;  $12o00x  {G8^%+Jf.)=$8593.75.  Ans. 

(45)  $3000x  (108^%-f  J%)=$8670,  Ans. 

(46)  $100X55=$5500;  $5500x28|%=$1581.25 ; 
$l581.2o-f-$13.75=$l,595,  Ans. 

(47)  $100  X  50=$5000  ;  $5000  X  108}=$5412.50 ; 
$5418.75— $5412.50=$125 ; 
$6.25-r^5000=.00  Y25=lfc ,  Ans. 


STOCKS  AND  BONDS.  109 

(48)  35X$100=$3500;  ($3500x108-1)— ($3500  X86^)=$761.25, 

Ans, 

(49)  ia5x$100=$13500;  $13500x  (100%— 15 J ^)=$1 1407.50, 

Ans. 

(50)  $3V90-T-(100%— 5J%)=$4000;  $4000-f-$100=40,  Ans. 

(51)  5%  of  [$4196.25-T-(93%+J%)]=$225,  Ans. 

(52)  6%  of  ($1299-^37i%)=$209.23+,  Ans. 

(53)  $4,696.95-r-(45%+i%)=$10380; 
$622.80-i-$10380=6%,  Ans. 

(54)  6%  of  ($5000-f-75%)=$400; 
bfo  of  ($5000-j-60%)=$416§; 
$416§— $100=$16|. 

5%  at  60 ;  $16f  better,  Ans. 

(55)  $11212.50-4-112J%=$10000; 

6%  of  $10000X106|%=$641.25,  Ans. 

/  6/.  \       /   h% 

(56)     —    Xl08|%)=l+%;  6%at90,ANS. 

\90%/       \95% 

(57) =zUfo\  6%  at  90,  Ans. 

90^      125% 

1%         6% 

(58)    X =N.  Y.  7'sy\'V%,ANS. 

105%     98% 

(59)  7%=15%;  100%=214f%,  Ans- 

(60)  6%-T-90%==6f%; 
225X6|%=15%,  Ans. 

(61)  6%  of  $5000=$300 ; 

$5000x115 

5%  of =$273.8C-  f  ; 

105 
$300— $273.804-=$2fi.20  loss,  Ans. 

(62)  $1.00-^125=.80,  Ans. 


1  lo  STOCKS  AND  BONDS, 


(64)    108X7^=7.56%;  7.56^-6 %  =126,  Ans. 

(65) =^h;  jfj=$o;  Iff  orl00%=$1615,ANS. 


(66)  $1500-T-6  %  =$25000  ; 
$25000X(96|%4-J%)=$24,250,  Ans. 

(67)  $10200^-30%  =$34000.     $34000x6%  =$2040,  Ans. 

(68)  10%-j-125%=8%,ANS. 

(69)  $1.00-^150%=66f%,ANS. 

(70)  6fc=7j%fe;  100%=121f,  Ans. 

(71)  lO^of  $50=$5;  9%=$5;  100%=$55f,  Ans. 

(72)  $420-^-105%  =$400. 
$400  X 125  %  =$500,  Ans. 

(73)  6%  of  $200=$12. 
$I2-r-$150=.08=8%,  Ans. 

(74)  $29,840-r-93i%=$32,000:  6%  of  $32,000=^1^20, 
$29,840— $240=$29, 600. 
$1920-4-$29,600=6^f  %,  Ans, 

(75)  $8475-T-113%=$750r, 
5%  of  $7500=$375. 
$375X110% 
=$206.25,  ans. 

2 

(76)  5%  of  ($7540-^104 %)=$362.50. 

J  of  ($362.50X128%)=$232,  Ans. 

(77)  '^Mo-^lOifc^li^fcANS. 

(78)  6%=8%;  100%=133^%,Ans. 

(79)  $276-T-115%=$240;  $240x2=$480. 
$480-T-$9600=.05=5%,  Ans. 


STOCKS  AND  BONDS. 


(80)  $8500X115%=$9775,  Ans. 

(81)  $26,250-^106^%=$24,647ff. 
$24,647ff  X 109  ^  =$26,866}f 
$26,866^1— $26,250=$616}f,  Ans. 

(82)  $8000X110^%  =$8810,  Ans. 

(83)  $2240-7-1 12%  =$2000  face  of  stocks. 
$2000X{100%— 20%)=$1600,  Ans. 

(84)  100%-T-125%=80%;  100%— 80%=20%,  Ans. 

(85)  6%  of  {$6840-r-95%)=$432,  Ans. 

(86)  $1 1212.25^112  J  %  =$10000;  6%  of  $10000=$600. 
$600xl06f  %=$641.25,  Ans. 

(87)  $300.87^^(20 %4-f%)=$1458ff,  Ans. 

(88)  .075  of  l.-f.015=.076125;  .025%  of  .076125=.001903125. 
.001903125-i-1.015=.001875=j%%,  Ans. 

(89)  60 %  of  55  %  =33  % ;  7  %  H-33  %  =21/^  % ,  Ans. 

(90)  $2700-f-(100^,— 25%)=$3600;  $3600X8%=$288. 

10% 

$288-? =$2764.80,  Ans. 

100%— 4% 

(91)  100%— 15%=85%;  85% X 115%  =.9775. 
100  %  —97.75  %  =2\  % ,  Ans. 

(92)  105%^(100%-10%)=W-;  -W-^102=}||. 
$33-v-102%=$32x6y;  %Z2^j—%li=%2l^^. 
Hf-ifl=r¥3;  t¥3=$21^;  if  f=$148.50,  Ans. 

(93)  100%— 94%=6%;  6%=$666;  100%=$11100. 
$11100-=-$50=222,  Ans. 

(94)  72  X  $1000=$72000 ;  $72000  X 106^  %  -^($500x  102  %)=150, 

Ans. 

(95)  4%  =$300;  100%  =$7500;  $7500x92%  =$6900,  Ans. 

(96)  6  %  =$180 ;  100  %  =$3000  ;  $3000  X 102  %  =$3060,  Ans. 


112  STOCKS  AND  BONDS. 

(97) =U.  S.  4fs/^\^,ANS. 

106%      99f% 

(98)  $75  X  92  %  =$69 ;  $69  X  18=$1242,  Ans. 

(99)  $100X15=$1500;  $1500Xll8%=$1770,  Ans. 

(100)  $100X9=$900;  $900x85=$765. 
$100  X  8=$800 ;  $800  X  98=$784. 
$784— $765=$19,  Ans. 

(loi)   $100X23=$2300;  $2300x102%  =$2346,  Ans. 

(102)  $50X18=$900;  J%+|%=|%;  |%  of  $900=$11.25,  Ans. 

(103)  $10X120=$1200;  l\%-\-l%=l\\%\  Ifi^  of  $1200=$23, 

Ans. 

(104)  82%-65%=17%;  17%+5^%=22|%  gain. 

22J%=$1125;  100%  =$5000. 
$5000-^$  100=50  shares,  Ans. 

(105)  21%  =$945;  100%  =$42000;  $42000-t-$100=420  shares 
86  J  %  —73  % =13  J  % ;  13^  %  of  $42000=$556o. 
$5565+$945=$6510  gain,  Ans. 

(106)  $9040-T-113%  =$8000  stock. 
5J%  of  $8000=$440. 
113%— lll|-%=li%  loss. 
1^%  of  $8000=$120. 
$440— $120=1320,  Ans. 


DISCOUNT.  113 


DISCOUNT. 


(i)   4%  of  $1  for  4  yrs.=.16 ;  6%  of  $1  for  4  yrs,=.24 
$25-T-(iyi-xV'V)=$449.50,  Ans. 

(2)  Amt.  of  $1  at  4^%  for  8  mos.=$1.03. 
$156-^$1.03=$151.45+. 

$180-4-$i5i  .45+=$28.55— . 

$28.55 r-$151.45-h=123VV^%  nearly,  Ans. 

20  Hi 

(3)  — =1;  %-%=\\  i=iH%;  — =lyr. 
22^  20 

1X360=200  days,  Ans. 

(4)  1%  a  month=10%  per  annum. 
Bank  discount  of  $1  for  6  mos.  3  da.  at  10%=|. 
$1— $.0508J=$.9491|. 
$4800-^$.9491§=$5057.06+,  Ans. 

(5)  $1804-$13.90=$193.90. 

Bank  dis.  on  $1  at  6%  for  6  mo.  3  da.=.0305;  $1— .0305= 

.9695. 
$193.90-T-.9695=$200,  Ans. 

(6)  Simple  int.  on  $1  for  3  yr.  4  nio.=.08^. 

True  discount=.07x% ;  .08|— .07x33=.00ff=|f%  rate. 
$65— 160=$5;  $5-^.00ff=$780,  Ans. 

(7)  8%  of  $1  for  1  yr.=.08  ;  I  wish  to  receive  9^. 

Then  f  must  be  what  is  left  after  discount  is  taken  out ; 

|-|=i=lH  cts. 

— =  time  which  equals  to  1  yr,  4  ©o,  20  da.,  Ans. 
8  ^  ^ 


114  DISCOUNT. 


(8)  $405— $30=$375. 

1  %  of  $375  for  10  mo.  20  da.=$3^. 
$30-4-$3|=9%,  Ans. 

(9)  \  of  $3275.60=$1637.80. 

Int.  on  $1637.80  for  63  da.=$2.866. 

$1637.80— $2,866=$!  635.03. 

$1637.804-$1635.03=$3272.83+,  Ans. 
(lo)  31  gal.  2  qt.X  50=1575  gal. 

1575  X  $2.40=13780. 

Int.  on  $3780  for  93  da.  at  7^%=$73.24— . 

$3780— $73.24— =$3706.76,  Ans. 
(ri)   $1  at  8%  for  100  days=.02f ;  $l-|-.02f=$1.02g. 

$999H-$1.02f=$977.27+,  Ans. 

(12)  Am't  of  $1  for  183  da.=$1.0305. 
$185.49-T-$1.0305=$180,  Ans. 

(13)  1%  of  $326.40  for  7  yr.  9  mo.  10  da.=$25.386f. 
$114.24-f-$25.386|=4^%,  Ans. 

(14)  $340— $336.43=$3.57. 

6%  of  $340  for  1  yr.=$20.40. 
3.57 

X  360=63  da. ;  63—3=60,  Ans. 

20.40 

$45 

(15)  2  yrs.=24  mo. ;  $45-f-24= ; 

24 
$45 
24—10=14  mo.;  — X  14=$26i,  Ans. 
24 

(16)  1%  of  $396  for  60  da.=.66. 
$3.96-^.66=6%,  Ans. 

(17)  Am't  of  $1  at  9%  for  10  mo.  20  da.=$1.08. 
$105-f-]  .08=$375 ;  $405— $3.75=$30,  Ans. 

(18)  8%  of  $750  for  one  yr.=$60. 
8.50 

X360=5l  da. ;  51—3=48,  Ans. 


60.00 


DISCOUNT,  xt^ 


(19)  Am't  of  $1  at  6%  for  4  yrs.  8  mo.  10  da  — $1.28^. 

$l-v-$L28i=.78yV^ ;  $1— .78yV9=-21fii. 
$169^.21f|i=$769 ;  $769— $169=$eO0,  Ans. 

(20)  $2366.80-|-$33.20=$2400 ; 
6%  of  $2400  for  1  yr.=$144. 
33.20 

X360=83  da.;  83—3=80=2  mo.  20  da.,  Ans. 

144 

(21)  $245— $105=$140 ;  8%  of  $140  for  1  yr.=$11.20. 

105 

=9  yr.  4  mo.  15  da.,  Ans. 

11.20 

(22)  $800— $792=$8 ;  1%  of  $800  for  45  da.=$l. 
8-7-1=8%,  Ans. 

(23)  6%  of  $1  for  63  da.=$.O105  ;  $1— $.0105=$.9895 
$1385.30-j-$.9895=$1400. 

11400— 11385.30=$14.70,  Ans. 

(24)  1%  of  $2600  for  63  da.=$4|^  ;  $27.30-^$4|^=6%,  Ans. 

(25)  6%  of  $1  for  63  da.=.0105;  $72.66-7-.0105=$6920,  Ans. 

(26)  From  Feb.  19,  1892,  to  Jan.  1st,  1893,=10  mos.  12  da. 
Amt.  of  $1  at  8%  for  10  mo.  12  da.=$1.06||. 

From  Oct.  12, 1892,  to  Jan.  1, 1893,=2  mos.  20  da. 
6%  of  $1.06ii  for  2  mo.  20  da.=.0142x\. 
$1.06^4 -.0142x25=$1.0551^. 
$105.51J-=-$1.0551i=$100,  Ans. 

(27)  10;^  on  $1  for  6  mo.  3  da.=.0508J. 
$1— .0508^=. 9491§. 
$l500-7-.9491  §=$1580.33,  Ans. 

(j8)    Am't  of  $500  at  6%  for  3  yrs.=$590. 

Am't  of  $1  at  8%  for  3  yrs.=$1.24. 

$590-r-$1.24=$475.81— P.  W. 

$590— $475.81— =$114.194-Dis.,  Ans. 
(29)    Am't  of  $300  at  8%  for  2  yrs.=$348. 

Pres.  worth  of  $348  for  2  yrs.=$310.71. 

$348— $310.71=$37.29,  Ans. 


ii6  DISCOUNT. 


(30)  Am't  of  $1  for  5  mo.  at  \^Jo=%\M\ ; 
$3G8.75-^|1.04i=$354  P.  W. 
$368.75— $354=$14.75  Dis.,  Ans. 

(31)  Am't  of  $1  at  10%  for  4  mo.=$1.03^ ; 
$775-T-$1.03^=$750,  Ans. 

132)    Am'tof  $1  at6%  for8mo.=$1.04; 
$260h-1.04=$250,  Ans. 

(33)  5%  of  $2480=1124 ;  $2480— $124=$2356. 
Am't  of  $2356  at  10%  for  4  mo.=$2434.534-. 
$2480— $2434.53=$45.47,  Ans. 

(34)  xk— T77=tV7^;  $2.45h-xV7%=$535,  Ans. 

(35)  Am't  of  $1  for  10  mo.  at  12%=|1.10 ;  $1221-r-$1.10=$1110. 
$1122— $1110=$12,  Ans. 

(36)  Am't  of  $1  at  8%  for  9  mo.=$1.06. 
$840.40-r-$1.06=$792.83,  Ans. 

(37)  Int.  on  $1  at  1^%  a  mo.  for  33  da.=.0165. 
$1— .0165=.9835;  $1650-f-.9835=$1677.68,  Ans. 

(38)  Int.  on  $1  for  43  da.  at  8%=$.009f. 
$1— .009f=.990f. 
$2072.60-r-.990f=$2092.60—  Ans. 

(39)  20%  of  $100  for  63  da.=$3.50. 

Int.  on  any  sum  for  63  da.  at  l%=y^oW 
$3.50^-3-2%V^of  $103.50=19/<f^%,  Ans. 

(40)  Am't  of  $1  at  25%  for  1  yr.=$1.25 
$1^$1.25=.80;  $1.00— .80=.20=20%,  Ans. 

(41)  $10296 -f-3=$3432 ;  the  am't  of  the  present  worths  of  $3432 

for  1,  2  and  3  yrs.=$8620 
$8620— $8000=$620,  Ans. 

(42)  Int.  on  $1  at  6%  for  33  da.=.0055. 

$1— .0055=.9945 ;  $400h-.9945=$402.21,  Ans. 

(43)  rf 7ir=bank  discount ;  y^^=true  discount. 

$3.60^3a^G^%=$1060,  Ans. 


EXCHANGE.  117 


EXCHANGE. 


(i)   6%  ou  $1  for  8?  -ia-^-OlOS. 
L        (1.+^%)— .0i05=.9945. 
\        $5680X.9945.-=|5648.76,  Ans. 

(2)  $l+|%=$1.00f  ;  int.  on  $1  for  33  da.=.0055. 
$1.003— .0055=$!  .002. 

I        $1575X$1.002=$1578.15,  Ans. 

(3)  %\\-\\%=%\S)\\\  $1  at  6%  for  63  da— .0105. 
$2625X  ($1.01J— .0105)  =$2636.81+,  Ans. 

(4)  Int.  on  $1  for  33  da.  at  6% =.0055. 
$500  X  ($1.01— .0055)  =$502.25,  Ans. 

(5)  Int.  on  $1  for  33  da.  at  6%  =.0055. 
$502.25-r-($1.01— .0055)=$500,  Ans. 

(6)  Int.  on  $1  at  8%  for  63  da.=.01f. 
$798.80-i  ($1.01^— .01|)=$800,  Ans. 

(7)  Int.  on  $1  at  6%  for  33  da.=.0055. 
$352.62-7-1^1— m  ^ +.0055] )  =$360,  Ans. 

(8)  $1  at  6^  for  93  da  =.0155. 

$4800 X  (l.Olf— .0155)=$4791.60,  Ans. 

(9)  Int.  on  $1  at  6%  for  63  da.=.0105. 
$1— (.02J+.0105)=.9645. 
$512.36-T-.9645=$531.218+. 

(10)    Int.  on  $1  for  63  da.  at  6%  =.0055. 

$5400  X  ($1.005— .0055)=$5397.30,  Ans. 


1 18  EXCHANGE. 


(II)    Int.  on  $1  for  33  da.  at  6  ^=.0055. 

$1324.74-=-  ($1.01f— .0055)=$1309.03,  Ans. 

(i2)   $5075— $5000=475. 

$75  -^ $5000=1^  % ,  Ans. 

(13)  $890xl01i%=$901.12^,  Ans. 

(14)  $1800X99%  =$1782,  Ans. 

(15)  Int.  on  $1  at  7%  for  63  eLd..:=S)\^q^. 
$1400X  (102^%— .01xV^)=$1420.18^,  AlfS. 

(16)  Int.  on  $1  for  93  da.  at  10%=.025|. 
$2400X  (103%— .025f)=$2410,  Ans. 

(17)  Int.  on  $1  for  63  da.  at  6%  =.0105. 
$1650X(.98^— .0105)=$1607.92o,  Ans. 

(18)  $7900  ^101^%  =$7783.25,  Ans. 

(19)  $5000-5- .98|=$5076.14,  Ans.. 

(20)  Int.  on  $1  for  63  da.  at  6%  =.0105. 
$1000^(103%— .0105)=$980.87,  Ans. 

(21)  i"87x$4.82xl06%=$444.50+,ANS. 

(22)  $2000-^■($4.85xl06%)=/389  7d.4-,  Ans. 

(23)  $1505.40X(1.00— 1%)=$1501.64— ,  Ans. 

(24)  Int.  on  $1  for  63  da.  at  6%  =.0105. 
$12692.50X  (100|%— .0105)=$12654.42+,  Ans. 

(25)  $2000^1.00f=$l987.58— ,  Ans. 

(26)  $4681.25^(100%— li-%)=$4740.51-,  Ans. 

(27)  Int.  on  $1  for  21  da.  at  6%  =.003^. 
(I.OO4-.OO5— .003^)=1.001^. 
$5264.15-J- 1.001  ^=$5256.27—,  Ans. 

(28)  Int.  on  $1  for  24  da.  at  6%  =.004. 
1.00-(^%-f-.004)=.9872i. 
^6836.75 -^.9872f =$6925.04,  Ans. 


EXCHANGE.  119 


(29)    Int.  on  $1  for  63  da.  at  6%  =.01 05. 
].01|— .0105=$1.0045. 
$850X1. 0045=$853.82o,  Ans. 

'(30)    Int.  on  $1  for  33  da.  at  7%=.006iV 
$2128.525^-  (1.02— .006j\)=$2100,  Ans. 

(31)  Int.  on  $1  for  63  da.  at  6%  =.0105. 
$oOOX  (1.00|— .0105)=$498.50,  Ans. 

(32)  Int.  for  93  da.  at  6%  =.01 55. 
$343.22h-[1.00— (J-|-.0155)]=$350.404-,  Ans. 

(33)  Int.  on  $1  for  33  da.  at  6%  =.0055. 
$362x  (.98^— .0055)  =$354.58—,  Ans. 

(34)  Int.  on  $1  for  63  da.  at  6%  =.0105. 
$652.925h-  (1.01^— .0105)=$650,  Ans. 

(35)  Int.  on  $1  for  33  da.  at  6%  =.0055. 
$1588.595 X  (.98|—.0055)=$1560,  Ans. 

{36)  $1000x100^%  =$1005,  Ans. 

(37)  $3000x1011%  =$3037.50,  Ans. 

(38)  Int.  on  $1  for  33  da.  at  6%=.0055. 

\        $5000  X  (1 .00^— .0055)  =$4978.75,  Ans. 

(39)  Int.  on  $1  for  93  da.  at  6%— 0155. 
$1500X  (.991— .0155)=$1471.875,  Ans. 

(40)  $5000X991%  =$5985,  Ans. 

(41)  $3000 X100J%  =$3003.75,  Ans. 

(42)  Int.  on  $1  for  93  da.  at  6%  =.0155. 
$5000x  (l.OOJ— .0155)=$4928.75,  Ans. 

(43)  Int.  on  $1  for  2  mo.  at  6%  =.01. 
$1500x(1.00J— .01)=$1488.75,  Ans. 

(44)  Int.  on  $1  foi  4  mon.  at  0%— 02. 
$1500X  (1.00i%  — 02)=$1473.75,  Ans. 


12Q  EXCHANGE. 


(45)  Int.  on  $1  for  63  da.  at  6%  =.0105. 
$5000 X  (l.OOyV— .0105)=$4952.50,  Ans. 

(46)  $5000 -f- 101^%  =$4926.11—,  Ans. 

(47)  $5725-^  100 J^  =$5710.71+,  Ans. 

(48)  Int.  on  $1  for  33  da.  at  6%  =.0055. 
$1500-^(100^%— .0055)=$1506.40,  Ans. 

(49)  Int.  on  $1  at  9%  for  63  da.=.015|. 
$1200 -J-  (100|— .Olof  )=$1213.04+. 

{50)   $10000-^(100%— i%)=$10012.514-,  Ans. 

(51)  $1750^100J=$1747.81+,  Ans. 

(52)  Int.  on  $1  at  6%  for  33  da.=.0055. 
$3500-^ (100J%— .0055)=$3514.934-,  Ans. 

(53)  ($3762.50^-105^)  H-$4.87=/732  6s.  2.4d.4-,  Ans. 

(54)  ($2984.38^107^) -^-$4.86=^571  4s.  6.6d.-|-,  Ans. 

(55)  (3269-^5.15) X105|=$668.87-|-,  Ans. 
(56).  (8950-j-5.19)Xl06J=$1832.25—  Ans. 

(57)  (/895  10s.-f-4.87)Xl06f=$4650-f-,  Ans. 

(58)  (5725^5.20)  Xl06i=$]169.77-f-,  Ans. 

(59)  (^585  10s.  5d.^$4.86)Xl07^=$3059.05+,  Ans. 

(60)  (/875  5s.  4d.-f-$4,885)Xl04|=$4484.1lH-,  Ans. 


INSURANCE,  121 


INSURANCE. 


(i)   f  of  $36004-f  of  $6000=$7500.  \ 

($126— $1)  -4-$7500=lf  ^ ,  Ans.  1 

(2)  1J%=$75;  100%=$6000.  \ 
|=$6000 ;  |=$10000,  Ans.  \ 

(3)  I  of  $340000=1212500.  \ 
1%  of  $212500=$1328.12-f,  Ans.                                *        •  ] 

(4)  1J%=$17.25;  100%=$1380.  \ 
|=$1380 ;  |=$2300,  Ans.  \ 

(5)  11  ^=$39;  100^=$3250.  \ 
lfM=f,  Ans.  ' 

(6)  2i%  of  f  of  $24000=$337.50.  ; 
1^%  of  f  of  $36000=$270.  j 
$337.504-$270=$607.50,  Ans.  I 

(7)  f  %  of  $1275=$7.08;  $7.08J+$1=$8.08J,  Ans.  \ 

(8)  f  of  $4800=13200.  \ 
$19.20^$3200=f%,  Ans.  \ 

(9)  2%of  |=t%;  2l%oi\^Wo-  \ 

iV%-iV=t\%,AnS.  \ 

(lo)   $5000+$5000=$10000. 

|0Mfl=2.  i=$262.50;  f=$1181.25.  1 

$1181.25^$45000=2f^,  Ans.  \ 


Ii2  INSURANCE. 


(ii)   $19.95x5=$99.45  annual  payment.  \ 

($99.45X75— 2 1)=$5370.30,  Ans.  i 

(12)  $104.58X10==$1045.80.  \ 
Premium  is  paid  at  the  beginning  of  each  yr.  and  draws       j 

interest  for  10,  9,  etc.,  yrs.=55  yrs. 
Annual  int.  on  $104.58  at  6%  for  55  yrs.=$345.11. 

$1045.80-f$345.11==$1390.91-h,  Ans.  ' 

(13)  $118-^1%  =$14750,  Ans.  "^ 

(14)  $42.30-5-^9^%  =$4700. 

|=$4700;  |=$7520,  Ans.  ' 

(15)  |=$197.13;  |=$328.55;  2J%-2}%=J%;  '■ 
J  %  =$328. 55;  100%  =$131420.  i 

^  J=f  131420 ;  §=$262840,  Ans.  ^ 

(16)  J  of  l|%=f  %;  1\%  of  J=J%.  \ 
l|/«-(i%+l%)=T'o%;  t\%=^8.11;  100%=$19370,  Ans.      \ 

(17)  (1|%  of  $8000+2J%  of  $10000)+$^07.50=$560.  \ 
2  fc  =$560 ;  100  %  =$28000,  Ans.  \ 

(18)  f  of  $2000=$1500;  $1500^(100%— U%)=$1522.84,  Ans.  • 

(19)  1J%=$225;  100%  =$15000.  j 
f =$15000 ;  f =$20000 ;  ^+l=i  ;  ' 
§=$20000 ;  ^=$6666.66§ ;  '  ^ 
|=$13333.33i,  Ans.  \ 

(20)  $325-;- $16250=2%,  Ans.  J 

(21)  li%=$2475;  1000%  =$198000.  j 
§=$198000;  |=$297000,  Ans. 

(22)  2J%=$1657.50;  100%=$66300.  ; 
f  =$66300;  f=$88400,  Ans. 

(23)  4J%=$400;  100%=$8888|.  ■ 
§=$8888| ;  f=$13333.33A,  Ans.  i 

(24)  f  %  of  I  of  $30000=$168.75.  : 
$30000— ($5000— $168.75)=$25168.75,  Ans.                        «  .^ 


INSURANCE.  ii3 


(25)  3%=$180;  100^=16000. 
§=$6000 ;  I  =$9000,  Ans. 

(26)  $652.50-^$43500=l^%,  Ans. 

(27)  1^%=$175;  100%=$14000,  Ans. 

(28)  $21.10X5=$! 05. 50,  Ans. 

(29)  $123.90^$o000=2|ff^,  Ans.     , 

(30)  f  of  $1 50000=$1 1 2500. 
|%of  ^of  $112500=$135. 
1%  of  t  of  $112500=$210.93. 
$112500— ($28125+$22500)=$61875. 
1%  of  $31875=$371.25. 
$135+$210.934-$371.25=$717.18,  An3. 

(31)  1\%  of  $6000=$135  prem. 
65|%  of  $6000=$3945. 
$3947— $135=$3810,  Ans. 

(32)  $L10Xl500=$1650cost. 
$1.20X1500=$1800. 

(2^%  of  $lS00)+$1650=$169d. 
$1800— $1695=$105,  Ans. 

(33)  1%  of  $100000=$750. 
IK           i%  of  $60000=$525. 
I^P           $750— $525=$225,  Ans. 

(34)  3%=$378;  100%  =$12600,  Ans. 

(35)  $1950^(100%— 2^%)=$2000,  Ans. 

(36)  9700X$1.20=$11640. 
$11640^(100%— 3%)=$1200,  An3. 

(37)  $2600^(100%— xV%)=$2618.26-f-,  Ans. 


124  TAXES. 


TAXES. 


(1)  $486250X.00^^V=$3792.75,  Ans. 

(2)  $3800X.00xVV==$29.64;  $29.64+$l=$30.64,  Ans. 

(3)  $1.50X3=$4.50;  $53.46— $4.50=$48.96. 
$48.96 -^$8704=53^c.  on  $100,  Ans. 

(4)  2J^=$26.04;  100%=$104i.o0  income. 
16%=$1041.60;  100%  =$6510,  Ans. 

(5)  $7592-^(100%4-2%)=$7450,  Ans. 

(6)  $1.35=1.35%  on  the  dollar. 
$125127.66  -f-  (100  %  —1 .35  %  )=$126840  cap. 
1.35%  of  $126840=$1712.34  tax,  Ans. 

(7)  1024X$1=$1024. 
$4000— $1024=$2976. 

$2976 -T- 2.4  mills=$1240000,  Ans. 

(8)  $4300+$1940=$6240. 
$33.20— $2=$31.20. 
$31.20-^$6240=|% ,  Ans. 

(9)  3x%%  of  $6748950=$242962.20  amount. 
\\%  of  $242962.20=$3644.434-  fees,  Ans. 


DUTIES  OR  CUSTOMS.  7^5 


DUTIES  OR  CUSTOMS. 


(1)  1114-1124-113=336  lbs.;  6%  of  336=16.8. 
(336—16.8)  X  $.05=$15.96,  Ans. 

(2)  250  lbs. X 20=5000  lbs. ;  ^\%  of  5000  lbs.=312.5  lbs. 
(6000— 312.5) X|.20=$9375  ;  4^  of  $9375=137.50,  AnS' 

(3)  3724  yds.  Xl0c.=$372.40. 
11%  on  3724x23c.=$94.217. 
$372.40+$94.217=$466.617. 
$466.617X{100^— 10%)=$419.96— ,  Ans. 

(4)  45X36X$1.25=$2025. 

2%  of  $2025=$40.50;  $2025— $40.50=$1984.50. 
40^  of  $1984.50=1793.80,  Ans. 

(5)  98X12=1176;  10%  of  1176=117.6. 
(1176—117.6)  X  $.05=$52.92,  Ans. 

(6)  668X36=24048;  ^  of  24048=3435.42+. 
(24048—3435.42+)  X  |.02^=$515.31+,  Ans. 

(7)  30%  of  (40X3|X.75)=$35.07+,  Ans. 

(8)  760  lbs.  X  30=22800  lbs. ;  12%  of  22800  lbs.=2736  n>«\ 
22800  lbs.— 2736  lbs.=20064  lbs. 

(20064  lbs.-5-100)X$1.20=$240.76+,  Ans. 

(9)  $631.43— $53.84=$578.09. 

2%  of  1680  lbs.=33.4;  1680—33.4=1646.6. 
$578.09-v-(1646.6Xll5%)=30+cts.,ANS. 

(10)   $7389.03— $73.80=$7315.23. 

$7315.23-^130%=$5627.10,  Ans. 


Ti^  DUTIES  OR  CUSTOMS. 

(11)  60X54X$1.80=$5832. 
60X54X$.25=$810. 
5%  of  $5832=$291.60. 

20%  of  ($5832— $291. 60)=$1108.08. 
$5832+$810+$1108.08+$8.50=$7758.58,  Ans. 

(12)  50X220=11000  lbs.;  4%  of  11000=440  lbs. 
(11000— 440)  X$.05=$528. 

$l84.80-^$528=35%,  Ans. 

(13)  540X160  lbs.=86400  lbs. 

3*  %  of  86400=3024 ;  86400—3024=83376  lbs. 

83376  X$.09=$7503.84;  15%  of  $7503.84=$1125.57J.     A.ns. 

(14)  28%  of  (25X24X45X$1.13)=$8542.80,  Ans. 

(15)  12x42x$1.30=$655.20. 
5%  of  $655.20=$32.76. 

%^%  of  ($655.20— $32.76)=$196.07—,  Ans. 

(16)  40X160=6400  yds. 
20%=$1024;  100%=$5120. 
|5120-^6400=80c.,  Ans. 

(17)  20X25X.10=$50. 

15%  of  $50=$7.50. 

6%  of  ($50— $7.50)=$2.55,  ANS. 

(18)  2240X7X$.17X20%=$533.12,AN& 

(19)  20X63=1260  gal. 
oyo  of  1260=63  gal. 

(1260— 63) X$.09=$l 07.73,  Ans. 

(20)  10X145=1450  lbs. ;  8%  of  1450=116  lbs 
(1450— 116) x.06|=$90.04-f,  Ans. 

(21)  45X120=5400  lbs. 

10%  of  5400=540  lbs. ;  5400— 540-=4860. 
4860X$.10=$486,  Ans. 


PROPORTION.  12" 


(22)  210X190=39900  lbs. 

5%  of  39900=1995;  39900—1995=37905  lbs. 
25%  of  (37905 X$.05)=$473.81+,  Ans. 

(23)  40%  of  (15X25X35X$3.95)=$20737.50,  Ans. 

(24)  20%=$40.50;  100%=$202.50. 
$202.50  ^  (100  % —10  %  )=$225. 
15X12=180  doz.;  $225-^180=$1.25,  Ans.. 

(25)  25%  =$337.50;  100  %  =$1350  ; 
$1350 -^  100 Xl8=75c.  invoiced. 
.75X125%  X120%=$1.12^  S.  P.,  Ans. 

(26)  35%=$806.12;  100%=$2303.17+invoiced; 
$2303.17+ X 135% r-=$3.\09.274-cost,  Ano. 

(27)  $1473.80^$3684.50=40%,  Ans. 


PROPORTION. 


(1)  8.4 : 4.95  : :  9i :  5|,  Ans. 

(2)  lJ:9i::H:8iANS. 

(3)  f:T'i::|:^,ANS. 

(4)  (35—14) :  35  : :  24 :  40,  Ans. 

(5)  fXj=^V,ANS. 

(6)  6-^1^=5,  Ans. 

(7)  7000:5760  ::l:iH»  Ans. 

(8)  (3X5:4X9)— (1X2:6X7)=!^,  Ans. 

(9)  (7i-4f)-(4|^7i)=Ht^.  Ans. 
(10)   2Jx6^=14f,  Ans. 


12J 


PROPORTION. 


(11)  2J-5-6i=^c,  Ans. 

(12)  ^=ratio;  divisor  5  times  the  dividend. 
Then  there  are  4  parts  excess. 
Then  4  : 1  : :  1 :  J,  AnS. 

(13)  1 :  1| : :  40 :  120 ;  120—48=72  lbs.,  Ans. 

(14)  i  of  (3i-TV)=lM. 
3|-lM=lt^,  Ans. 

(15)  Their  money  is  as  1,  3  and  12 ; 
1+34-12=16. 
xV  of  $3456=$216  C ;  i\=$648  B ;  if=$2592  A,  Aks. 

(16)  |=f;  f=ff ;  204-21=41. 
If  of  2255=1100  A ;  f  f=1155  B,  Ans. 

(17)  l=f;  f=lf ;  ff-!f=i\. 

^\=120;  11=1176; 
f  1=1296,  Ans. 

(18)  |=t;f=V-;  V4I«=¥: 

-¥=itV;  1=1; 

¥=l.  •••  f  and  f ,  Ans. 

(19)  l=H;l=¥-;-V— f=f. 

|==$637;  f =$728  John. 
i/-=$1365  James,  Ans. 

{20)    5+8= 

(21)   The  cost  of  the  house,  farm  and  store  are  to  each  other 
as  1,  3  and  6. 
1+3+6=10. 
$450+$650=$1100. 
$28100— $1100=$2700C. 
tV  of  $27000=$270-.  .'.us-.' , 
(t^^  of  $27000) +$-l50=$8550  farri ; 
(^  of  $27000) +$650=$16450  store,  Ans. 


PARTNERSHIP.  129 


PARTNERSHIP. 


I 

I 


(1)  2^  of  $300=$G0  A;  if  of  $300==$144  B;  ^V  of  $300=$96  C, 

Ans. 

(2)  16+14-4-12=42 ;  if  of  $1200=$457f  X. 

If  of  $1200=^100  Y;  ||  of  $1200=$342f  Z,  Ans. 

(3)  $18000+$60004-$10000=$34000. 
$34000  X  (1 00  %  —30  % )  =$23800. 

$23800  X 1 50  ^^  =$35700 ;  $35700— $34000=$1700. 
if  of  $17uO=$900  A;  /j  of  $1700=$300  B;  ||  of  $1700= 
$500  C,  Ans. 

(4)  $2250— ($800+$1000)=$450  C's  gain. 
$450^$3000=15%  gain;  15%=$800;  100%=$5333J  A's; 
lo%=$1000;  100 %  =$66661  B's,  Ans. 

(5)  $6500+$8000+$5500=$20000. 

2V(y  of  $12000=$3900  sons  ;  ^^  of  $12000=$4800  wife ; 
2V0  of  $12000=13300  daughters,  Ans. 

(6)  $5000+$6500+$4500+$2500+$600=$19100. 
$23000— $19100=13900. 

x^o  of  $3900=11218.75  A ;  y^V  of  $3900=$1584.37|  B ; 
^^  of  $3900=$1096.87|  C,  Ans. 

(7)3X16=48  ^Vj  of  $87.20=$19.20  X 

5X20=100  if  I  of  $87.20=140  Y 

7X10=  70  -gVV  of  $87.20=$28 

—  $87.20-^218=40^  per  week,  Ans. 

(8)   $4200-i-$3600+$4500=$12300. 

iVa^  of  $2706=$924  A ;  -j^Jv  of  $2706=$792  B ; 
xVj  of  $2706=$990  C,  Ans. 


I10  PARTNERSHIP. 


(9)   7X30=210  $1600— $95=$1 505. 

5X40=200  \\\  of  $1505=1525  A  ; 

6X32=192  \%\  of  $1505=$500  B  ; 

\%\  of  $1505=$480  C,  Ans. 

oOi^ 

(10)  $125-f-$625=18if%. 
$810Xl8if%=$150;  $125+$150=$275,  Ans. 

(11)  $2500X24=$60000 
$3000X22=$66000 


$126000 
tY^  of  $2835=$1350  A ;  -^^^  of  $2835=$1485  B,  Ans. 

(12)  $3000— $2730=$270. 
10+12+14=36;  \%  of  $270=$75  A; 

\\  of  $270=$90  B ;  If  of  $270=$105  C,  Ans. 

(13)  7.5+1=7.875. 

7  5  # 

_—  of  756=720 ;  of  756=36,  Ans. 

7.875  7.875 

If 

(14)  lt+2i=4J ;  -  of  10.25=4.1 ; 

4^ 

—  of  10.25=6.15,  Ans. 
4i 

(15)  $100X150%  =$150;  50=gam. 
$50— ($18+$19)=$13  C's  gain. 

50%=$18;  100%=$36A;  50%=$19;  100%=$38B. 
50%  =$13;  100  %  =$26  C,  Ans. 

(16)  8X23=184  iM=A^A 
12X29=348                         IM=T3V  B,  Ans. 

532 

(17)  210+140=350;  ||^  of  $50=$20,  Ans. 

(18)  80X60=4800  ^-^  of  $50=$30  A 
64X50=3200  ff  of  $50=$20  B,  Ans. 

8000 


PARTNERSHIP.                                131 

(19) 

12500  X18=$45000 

lYr  of  $325C=$1250  A 

^^ 

$1500x18=127000 

1V7  of  $3250=$750  B 

h 

$5000  X  9=$45000 

x^rV  of  $3250=11250  A,  Ans. 

1                  $117000 

(20) 

80X6=480 

720+9004-300=1920. 

40X6=240 

■j-V2<V  of  $275=$103.12|  A 

^^i~^  of  $275=$128.90|  B 

720  A 
100X6=600 

i^i^  of  $275=$42.96i  C, 

Ans. 

50X6=300 

900  B 

50X6=300  C 

(21) 

4X3=12 

36+48|=84f 

fof  4xy=24 

36A 

36 

of  $1695=$720  A 

84f 

5X3=15 

m 

1  of  5X9=33| 
48|B 

48| 

of  $1695=$975  B,  Ans. 
84| 

■m 

Capital  is  as  6,  4  and  3 

9 

H 

6X4=24 

t:\V  of  $1988=$714  A 

A 

3X9=27 

x\\  of  $1988=$728  B 

■ 

51  A 

f  j\  of  $1988=$546  C, 

Ans. 

■ 

4X13=52  B 

■ 

3X13=39  C 

P 

142 

I 


(23)    $5600X12=$67200 
$4200X12=$50400 


$16800 
$16800-^(12— 4)=$2100, 


Ans. 


EQUATION  OF  PAYMENTS. 


(24)  404  X  50c.=$202 
340X  $1.10=1374 

$576 
f  ^f  of  $31.68=$11.11  A 
lif  of  |31.68=$20.57  B,  Ans. 

(25)  $7000X6=142000. 
\\—^T=^ix ;  $42000-^T«x=$77000. 
($77000— $42000) -v-|5000=7  mo.,  Ans. 


EQUATION  OF  PAYMENTS. 


(1)  ll-f-104-9,  etc.  to  1  mo.=66  mos. 

$50  paid  the  first  of  each  mo.  is  $3300  for  1  ma 
$3300-j-$600=5f  mo.,  Ans. 

600     2 

(2)  $900— $300=$600.    =-; 

900    3 

2  3 

-=12.    -=18  mo.,  Ans. 

3  3 

(3)  30  X  0=  0 
80X12=  960 
70X24=1680 
60X40=2400 

240  )5040(21  da.=Feb.  5th,  Ans. 

(4)  $300X  0=  0 
$700 X  72 X  50400 
$800X144=115200 


1800  )  165600(92  da.=Aug.  1st,  Ans. 


EQUA  TION  OF  PA  YMENTS.  133 


(5)  $500x4=2000 
$600X5=3000 
$400X7=2800 

1500         ) 7800(5  mo.  6  da.,  Ans. 

(6)  $  900  X  12=  10800 
$1000X193=193000 
$1100X255=280500 


3000  )484300 (161.4+  or  162  da.=June  llth,  AnS. 

(7)  $500  X  4=  2000 
$500X26=13000 

1000  )  15000(15  da.=May  15th,  Ans. 

(8)  $  300X14=    4200 
$6000X35=210000 


6300  ) 214200  (34  da.,  Ans. 

(9)   $2000X4=  8000  $10500  X6=$63000 

$4500X2=  9000  6500  17000 


$6500  17000  4000  )46000(11|  mo.,  Ans. 

(10)  iof$10000=$2500 
|of$10000=$2000 
$2500  X  6^  15000 
$2000X18=  36000 
$5500X30=165000 


10000  )216000(21f  mo.=l  yr.  9  mo.  18  da.,  Ans. 

(II)  $  600X  5  =  3000 
$1000X10  =10000 
$1200  X  7|=  9400 


2800  ) 22400 (8  mo.,  Ans. 


134 


EQ  UA  TION  OF  PA  YMENTS. 


(12)  $  300x4=  1200 
%  800X5=  4000 
$1000X8=  8000 


2100    )  13200  (6f  mo. ,  Ans. 

(13)  $300x30=  9000 
$600x60=  36000 
$900X90=  81000 


1800 


(14)  $840  X  0=  0 
$400X94=37600 
$200X63=12600 


)  126000(70  da.=Aug.  10th,  Ans. 

$840— ($400+$200)=$240 


50200 


(15)   J  of  $12000=$4000 
\  of  $8000=$2000 
\  of  $8000=$4000 


50200 ^$240=209  da. 
209  da.  after  Oct.  3rd  is  Apr.  30tli 
next  yr.,  Ans. 

$12000— $4000=$8000 
$8000— $2000=16000 
$4000X3=$12000 
$4000X6=$24000 


$36000-5-6000=6. 

6^3= 

$36000 
=2  mo.,  Ans. 

(16) 

$  300X10=  3000 
$  500X25=12500 
$1000X40=40000 

$600x0=      0 
$550X1=  550 
$650X2=1300 

1850)55500(30  da., 

,  Ans. 

1850 

(17) 

1           3 

-X3=- 

4           4 

1 

-X6=3 

2 

1 

-X8=2 

4 

1        )5|(5|  mo.,  Ans. 

ALLIGA  TION. 


353 


(18)   $400X6=2400 
$600X8=4800 


7200        7200h-900=8  mo.,  Ans. 


(19)   $200x4=  800 
$200x2=  400 


1200        1200^200=6  mo.,  Ans. 


ALLIGATION. 


(I) 


(3) 


(5) 


3X10=  30 
5X  8=  40 
2X15=  30 

10  )100(10cts.,ANS. 


7^ 


5 

2^ 

1 

6 

H 

5 

7 

\ 

5 

10 

— 

2| 

5 

(2) 


(4) 


12 


16 


Ans. 


12 

4 

1 

15 

1 

2 

18 

2 

1 

20 

4 

1 

Ans. 


Ans. 


Note. — A  simple  solution  for  problems  of  alligation  med- 
ial is  to  write  the  differences  conversely  opposite  the 

31 


numbers  compared,  as,    |3 
4 

17 


which  shows  that  for  every 


3  at  3  cts.,  1  at  7  cts.  must  be  taken. 


13 


1X25 
1X25 


(6) 


6    3X25  Ans. 


67 


3X5=15 
3X5=15 
3X5=15 


14X^ 
14=5 


(0 


Ans. 


136 


ALLIGATION. 


(7) 


(9) 


80 


Ans. 


$450^5=190 
$90-^10=19 
4( 


Ans. 


(II)     $48-^60=80^^^. 


(12) 

(13) 


30 

50 

10 

1 

40 

40 

8 

1 

80 

— 

2 

85 

5 

1 

4 

(8) 

10 

8 
9 

12 
15 

2 
1 

2 
5 

150  at    8^ 

60  "     ^f 

30  "  12^ 

60  "  15^,  Ans. 

(lO)         , 

33 

1533 
28 
30 

35 

-r- 

5 
3 

2 

100=33  cts. 

5      ^V  of  100=20 

3 

X  of  100=12 
17 

—     II  of  100=68 
25                      Ans. 

of  80=20  chickens. 

of  80=20  ducks. 

I  of  80=40  geese,  Ans. 
$1X5=$5;  $5-f  $.04=15.04 ;  $5.04^7=72  cts.,  Ans. 

(14) 


(15) 


4  gal.  of  whiskey=$2.00 
\  "  "  alcohol=  .80 
1     "     "         water=       0 

h\  $2.80 

$2.80-^5^— 50|a  cts. 

Ans. 
15^  7f=1.935 
"     10^=  .024 
6^=1.163 


Ans. 


\ 
8 

23| 


3.122 


23i^-  3,122=7/^r-,  Ans. 


ARITHMETICAL  PROGRESSION.  137 


ARITHMETICAL  PROGRESSION. 


(i)   3X(19— l)-f50=$1.04,  Ans. 

(2)  2X(20— 1)=38;94— 38=56,  Ans. 

(3)  tVX(37—1)=21;  21+43=64,  Ans. 

(4)  180X11=1880;  $939— $880=$59. 
$939+159=1998;  $998Xl2=$11976. 
$11976-^2=$5988,  Ans. 

(5)  First  term  4  ;  com.  diff.  4  ;  uumb.  terms  100.     (100— 1)X4 

=396 ;  4+396=400  last  term. 
(400+4)  X 100 
=20200  yds.=llfi  mi.,  Ans. 

2 

(6)  (1000—1)  X  10=9990 ;  9990+10=10000  last  term. 

\  ($100.00 +$.10)  X1000=$50050,  Ans. 

(7)  (10— 1)X10=$90;  90+20=110; 
\  (1 1 0+20)  X  10=$650,  Ans. 

(8)  (10— 1)X  1^=13.5;  13.5+2.5=16  in.,  AiiS. 

(9)  (4+49)  X 10 


-=265,  Ans. 


(10)   3  yrs.  10  mos.=46  mos. 
60—21=39;  20—5=15. 
39^15=21  com.  diff. 
(5-l)X2f=10|. 
21— 10f=10|  first  payment. 

(46—1)  x2f =$108 ;  $108+$10.60=$118.60  last  payment 
J  (10.60+118.60)  X  46=12971.60,  Ans, 


138  GEOMETRICAL  PROGRESSION. 


'3 

i 

1 

GEOMETRICAL  PROGRESSION.  \ 


(1)  (I)  ^  X  9(.>=30|  mi.,  Axs. 

(2)  192 -^128=1  J  ratio; 
(li)  «X  128=1408,  Ans. 

20 

(3)  ^5=ratio;   =200  rds.,  Ans. 

(1— r%) 

(4)  C2)t=^<>-'>=524288. 

I X  524288=262 144  last  term.  - 

(262144X2)— i=o24287i. 

524287^^  (2— l)=o24287^  cts.=$5242.87J,  Ans. 

(5)  9thterm=7th;  (6)^=46656. 
16x46656=746496,  Ass. 

(6)  (I) -X  1024=13611,  Ans. 

(7)  iH-a— J)=2,Ans. 

(8)  |-^a-f)=8i.Ai^ 

(9)  512^8=64.    ^^^^^4,  Ans. 

(10)  27X3=81.    \/8l=9,  or  *-i/27T3=3;  3X3=9,  Axs. 

(11)  32-5-4=8.    ^^^§=2. 
4X2=8; 

8X2=16.    8  and  16,  Ans. 


TIME,  139 


TIME, 


(1)  1=1 ;  l=H ;  !^-f^M ;  12^^=8  o'clock  p.  m.,  ans. 

(2)  i=|;  1=1;  #4-1=1;  12^1=4  o'clock  P.M.,  Ans. 

(3)  A=H;H=W;W-M=fl;i2-fl=i0o'ciockA.M.,ANs. 

(4)  A=H;  ii=W;  ¥f-f-M=W. 

12-4-^5^6=40  min.  past  3  p.  m.,  Axs. 

(5)  l=A;  i=i;  i+f=!;  i2^f=8. 

12 — 8=4  o'clock  P.  M.,  Ans. 

(6)  If— t'i=H;  3o-f-i|=38T2x  min.  after  7,  Ans. 

(7)  1=2%;  'h^h\  fH-i=5=lf 

12-^||=9f ;  12— 9f=2i  o'clock  P.  M.,  Ans. 

(8)  I=/t;  1=1;  l+f=¥;  i2-^V=~f- 

12 — 7f=4f  or  17}  min.  after  4  p.  M.,  Ans. 

(9)  l=A*5;l=H;  M+H=f|. 

36^ff=22f ;  36— 22|=13J  or  \\  o'clock  a.  m.,  Ans. 

(10)  i=J;  |=J;  \-^\=\\  12^1=8  p.  M.,  ANS. 

(11)  ^  of  12=ff  hr.— 90  min.=3||  hrs. 
3|^  lirs.=57^  min.  past  3  p.  m.,  Ans. 

(12)  if— x^^H;  22-^H=-24min.,ANS. 

(13)  46  min.  to  gain. 

46xft=^^i^  iiiiii- 

60— o0x23-=9y^  min.  before  10,  Ans. 

(14)  1  |_J^=^i.     From  12  to  4=20  min. 
20-5-1^^=213^  min.  past  10,  Ans. 


lik  APPLICATION  OF  SQUARE  ROOT. 


(i5>    Minute  hand  must  gain  10  and  30  min. 
10xH=10ti  niin.  past  4. 
30xH=32A  iiiin-  past  4,  Ans. 
{i6i    The  hour-hand  is  40  minutes  +  a  certain  distance  (or  1 
space)  from  12.    The  minute-hand  is  ^  as  far  or  20  min. 
-\-\  space.     The  minute-hand  moves  12  spaces  to  1  of 
the  hour-hand.    20  min.-|-^  space  equals  12  spaces,  or 
20  minutes=ll^  spaces.     20-^llJ=l||  or  1  space.    12 
spaces=l||Xl2=20|f  min.,  Ans. 
(3)    The  hour-hand  is  10  min.-f-l  space  from  6.    The  minute- 
hand  is  (10  min.+l  space)  X  2=20  minutes-f-2  spaces  or 
50  minutes-|-2  spaces  from  12.     50  min.4-2  spaces=12 
spaces;  50  min.=10  spaces;  1  space=5  min.    5x12= 
60  min.  past  8  or  9  o'clock,  Ans. 
(17,    12—2=10.    30-^10=3  min. 

Min.  hand  travels  12  times  as  fast  as  hour-hand.     3x12= 
36  min.,  Ans. 
(i8i    H+^=!f ;  4-^-ff=2|;  4-2t=U  p.  m.,  Ans. 


APPUCATION  OF  SQUARE  ROOT. 


(1)  lA=160rds.    \/l60=12.64-f-rds.,  Ans. 

(2)  v/lOx  160=40  rds.,  Ans. 

(3)  \/lOAX  160=40  rds.  to  the  side. 
40X16^=660  ft;  660-5-15=44. 
44X4X140=170.40. 

44X4X5 

X  $6=$52.80. 

100 
$70.404-$52.80=$1 23.20,  Ans. 


APPLICATION  OF  CUBE  ROOT.  141 

(4)  v/2l6T6=6  in.,  Ans. 

(5)  Each   round   will   be  the  hypotenuse  of  a   right-angled 

triangle  whose  sides  are  8  ft.  and  G  ft.    \/8^-f-6^=10« 
o0h-6=8J  rounds;  10x8i=83J  ft.,  Ans. 

(6)  15X6=90;  18x6=108. 

v/(90)  24-  (108)  2=140.58+mi.,  Ans. 

(7)  20X160=3200. 
n/3200T2=40.     40X2=80. 
(40X2) +(80X2)  =240  rds.,  Ans. 

(8)  5408^2=2704.    \/2704=52  ft.  width. 
52X2=104  ft.  length,  Ans. 


(9)    \/(100)  2  4-(60)  ^+(26)  2=119.48+ft.,  An& 
(10)   y/\  of  (50)2=35.35+,  AnS. 


APPUCATION  OF  CUBE  ROOT. 


(1)  '^2150.4=12.9+in.,  ANS. 

(2)  1728xl5|='27000  cu.  in, 
\^27000=30  in. 
30X30X6=5400  sq.  in.,  ANS 

(3)  (1 6)  3—6=210  cu.  in.,  Ans. 


(4)   \^'^23lXl500=70.23+cu.  Jn. ,  hiA^. 


(5)   ^80Xl28=21.71+ft.,  Ans. 


142  MEASUREMENTS. 

(6)  192X27=5184. 
1X4X6=24.    5184-^24=216. 

^2l6=6  ft.  depth ;  6x4=24  width ;  6x6=36  length,  Ans. 

(7)  13^=¥;¥-32=f|. 

^^=1;  fX  1=1  ft.=9  in.  square. 
\  X  32=24  ft.  length,  Ans. 

(8)  ^2048^4=8  ft,  Ans. 


(9)   ^729X8=18  ft.,  Ans. 

(lo)   2150.4X100=215040. 
215040^3=71680.. 

^^^7l680=41.534-in.=3.464-ft.  height  and  width. 
3.464-X3=10.88-i-ft.  length,  Ans. 


MEASUREMENTS. 


(1)  (6)2X3.1416X10=1130.976  cu.  ft. 

(1 130.976 -f- 550) X  115=130.844-.  Ans. 

(2)  20X20X15=6000;  6000 -f- 450=1 3^  T.,  Awa 

(3)  30x20x20^550=21y\T,  Ans. 

(4)  10X5X8X12=4800  cu.  ft. 
4800X.8=3840bu.,ANS. 

(5)  1728X6.25=10799.8  cu.  in. 
10799.8^231=46.75-r-gai.,  ans. 

(6)  750-HlJ=600  bu.,  Ans. 


MEASUREMENTS,  143 

(7)    135 X. 8=108  cu.  ft. 

1X6X9=54.     108^54=2  ft.  depth. 

2  X  9=18  ft.  length.    18  -^  6=3  ft.  width,  Ans. 


(8)  ^583.2 H-. 8=9  ft,  AnS. 

(9)  10X4 X8X. 8=256  bu. 
lbu.-^l^pk.=3; 
256X3=768  bags,  Ans. 

(10)  (80x2JXlO)-f-24|=80|^P. 
80|§x$l.=$80|f,ANS. 

(11)  (45X2)  +  (60X2)=210. 

$254.54y«x-^ (210X8X 1  J-4-24|)=:|2.50,  Ans. 

(12)  (60-^3.1416) 2 X.7854X20X2J  cts.=99.5-4-  cts.,  Ans. 

(13)  8  in.=|  ft.    20Xf  X4=53J  ft,  Ans. 

(14)  16XUXl2=240ft,  Ans. 

(15)  (30)2=900.    n/900h- 3=17.32+ in.,  Ans. 
Or  side  :  diameter  of  cube  : :  1  :  \/3. 

.-.  30-^-^/3=17.32+ in.,  Ans. 

(16)  [(40—2)  3  X  .5236] ^231=124.37+  gal.,  Ans. 

(17)  (60) 2 X 3.1416 X. 02=1226.195+,  Ans. 

(18)  3.1416X5  cts.=$.15708. 
11005.312^  $.15708=6400. 
n/6400=80  in.,  Ans. 

(19)  $226.195^ [(60)  2  x3.1416]=2  cts.,  Ans. 

(20)  (2)  2  X  6  X  .50=112,  Ans. 


(21)  >/(4)2x(6)2=24;  24+36+16=76. 
TV\X4x20=42f  cu.  ft,  Ans. 

(22)  (3) 2 X. 7854=7.0686. 
(2)  2  X. 7854=3. 1416. 
\/7.0686  X  3.1416=4.7124. 
(4.7124+3.1416+7.0686)  X^  of  40^198,968+,  An^ 


144  MEASUREMENTS. 

(23)    (16) 2 X. 7854=201.064-. 
(12)  2  X. 7854=113.09+. 
\/201.06X  113.09=150.78. 
(201.06-1-113.094-150.78)  Xi  of  15=2324.65+ cu.  ft..  ANa 


24)    (8)  2=64 ;  (20)  2=400 ;  \/64  X  400=160  mean  base. 
64+400+160=624;  fffX  J  of  20=28f  cu.  ft,  Ans. 

(25)  \oi  (20+30)=25;  25-^12=2xV  ft 
10x2iVX4=83^  sq.  ft,  Ans. 

(26)  20^12=lf  ft;  (1§)2x20x|2.25=$125,Ans. 

(27)  (764) 2 xi  of  480=98391360  cu.  ft,  Ans. 

(28)  8h-2=4;  4x5x5=100;  5x5=25. 
100+25=125  sq.  ft,  Ans. 

(29)  \  of  8X80=320;  320x8=2560  sq.  ft 
$140.80-^2560=5^  cts.,  Ans. 

60X40 

(30)    X.05=$60,  Ans. 

2 

(31)  (30) 2 X. 7854x20X1728-^231=1057531  gal.,  Ans. 

(32)  (2)2X.7854X50X.20=$31.41+,  Ans. 

(33)  (2^) 2 X. 7854=4.90875. 

$3.927 H- (4.90875X1  X.10)=8  ft,  Ans. 

(34)  $27^(60X.20)=2.25. 
v/2!25=1.5  ft.=18  in.  square. 
\  of  18=2 ;  18—2=16  plank. 

16X60X1^  ft  wide=1440  sq.  ft,  Ans. 

(35)  6X2^X4=60. 

(2J)2=6^;  $3.31i-f-(60+6J)=5  cts.,  Ans. 


(36)  3  X  12=36 ;  V  (36)  2  --  2=25.45+  in.,  Ans. 

(37)  (14)2=196;  (\/l96— 2)2=98;  98x$2=196,  Ans. 

(38)  6280^3.1416=1680.67+  ft,  Ans, 


MEASUREMENTS.  145 

(39)  5280^3.1416=1680.674-  ft. 

(1680.67)  2  X  .7854=50  A.     148  P.  188.39+  sq.  ft.,  Ans. 

(40)  (100)  2  X  .7854X  .10=$785.40,  Ans. 


(41)   78544-.7854=10000;  v/iOOOO=100. 
100 H- 2=50  ft.,  Ans. 


(42)   n/(800)  2  —  (620)  2=505.57+  ft,  Ans. 


(43)  \/(40)  2— (10)2=38.72+  ft,  Ans. 

(44)  52x.7854x2=39.27sq.  ft. 
6X3.1416X30=471.24. 
(471.24+39.27—10)  X$.02=$10.01+,  AnS. 

(45)  20X63X231=291060  cu.  in. 
291060H-[(70)2X.7854]=75.63+  in. 
75.63-7-12=6  ft  3.63+  in.,  Ans. 

(46)  Capacities  are  as  12 :  (IJ)^ 

12 

= =1;  16X^=6^ 

6§x8=53^,  Ans. 

(47)  (15)  2  X  3.141 6=706.86,  Ans. 


(48)  >/l96Tj854=15.79+ in.,  Ans. 

(49)  (11)  2  X 3.1416=380.133+  sq.  ft.,  Ans. 

(50)  24X32X2=1536;  1536-hl00=15.36. 
$76.80-5-15.36=15,  Ans. 

(51)  9xl3x|Xli=131+fl.;  131-v-100=1.31+. 
1.31+X|1=|1.31+,  Ans. 


(52)  \/l520.5344  -^  3.1416=22  ft.,  Ans. 

(53)  39.27-4-3.1416=12.5. 
39.27X12.5=490.875  sq.  in.,  Ans. 


(54)  ^65.45-f-.5236=5. 

(5)2X3.1416=78.54  sq.  in.,  Ans, 


146  MISCELLANEOUS. 

(55)  (U) 3 X. 5236=1  cu.  ft.  391.5  cu.  in.,  Ans. 

(56)  \/(62)'-^— (20)2=48  ft. 
(48)2x3.1416=7238.2464  sq.  ft.=26.584-  P.,  Ans. 

(57)  3.1416X4X2^=31.416— ,  Ans. 

(58)  10+10^+14^=35;  35-j-2=17.5. 
17.5—10=7.5;  17.5—10.5=7;  17.5—14.5=3. 
\/l7.5X 7.5X7X3=52.5,  Ans. 


,5^    Ji5flZ=34,ANS.  \ 

(60)  16X8X2=256  \ 
14X8X2=224  '                  ' 

2)480(240 ;  240-^3=80  yds.,  AnS.  ; 

(61)  (6) 2 X.7854X 5^X1728=256505.35+.  \ 
256505.354-+(31iX231)=35.25+,  Ans.  ' 


MISCELLANEOUS. 


(1)  (100)2— (30)2=9100;  9100-v-(100x2)=45J,  Ans.  I 

(2)  10=G.  C.  D.;  40x30=1200  rds.  ' 
1200-i-(10)  2=12,  Ans.  j 

(3)  27  :  343  : :  (3)  :  ^K343=7,  Ans.  | 

(4)  Let  l=diameter  of  cheese.  1 
(1)  2  X  .7854=. 7854  area  of  whole  cheese.  \ 
The  square  of  the  sq.  rt.  of  \  of  1=.5,  area  of  largest  in-  \ 

scribed  square.  \ 

.7854 — .5=. 2854+  area  of  segments.  ' 

3X  4=12  lbs.,  four  segments ;  .2854  :  .7854  : :  12  :  38.02+  lbs.,  j 

Ans.  i 


MISCELLANEOUS.  I47 


(5)    (3)^:(H)'  : :  5  :  H  hr.,  Ans. 


(6)    n/(60)2— (30)2=51.96+ alt.  of  triangle. 

f  of  51.964-=34.64+  distance  from  corner  of  triangle  to 
the  center. 


n/(51.964-)  2— (34.64+) '^=38.73+  ft,  Ans. 

(7)  30X160X2=9600;  9600+ (100)^=19600. 
■v/l9600=140  sum  of  sides;  (100)2— (4800x2)  =400. 
^400=20  diff.  of  sides;  140—20=120;  120-^2=60  width ; 
60+20=80  length,  Ans. 

(8)  1  :  ^  : :  (9)2  :  40.5;  >/40r5=6.36+  in.,  Ans. 

(9)  36=G.  C.  D.;  1332^36=37;  37—1=36,  Ans. 

(10)  (5)3=125;  (125)2=15625,  Ans. 

(11)  102=100;  \/l00x2=14.14+;  14.14+10=24.14,  Ans. 

(12)  32—4=28;  (28) 2 xf  1=980  ft,  Ans. 

(13)  18X160=2880;  \  of  2880=960;  v/960=30.9+  rds.,  Ans. 


(14)  \/(36)2-r-3=20.7+in.,  Ans. 

(15)  v/(12)2-H3=6.9+;  [  (6.9)  3x1728] -^2150.4=266+ bu.,  Ans. 

(16)  %/8X  160X2=35.7+  rds.,  Ans. 

(17)  V\  of  136X17=34,  Ans.    . 

(18)  (16)  2+(4)  2=272;  272-r-(4x2)=34  ft,  Ans. 

(19)  49^X144=7146;  (1^)^X2=1;  7146— |=7141J. 
\/7l41iT6+l^=36  in.,  Ans. 

(20)  1  fur.=40  rds.;  v/(40) 2— (20)^=34.6+  alt  of  A. 
34.6+ X 20=692+  sq.  rds.;  692+ -^160=4.32+  A.,  ANS. 

(21)  [  (30)2X.7854]— [(20)2X.7854]=392.7+  sq.  ft,  Ans. 

(22)  A=length;  A— 12=width. 
(A— 12)  X  A=4  X 160  sq.  rds. 
\/A2—12A+36=v/ 640+36. 

...  A— 6=26 ;  A=32 ;  32—12=20,  Ans. 


1 48  MISCELLANEO  US:. 

{23)   20  raUs  per  rd.    4  sides=8Q. 

(rds.)2 

(80)2=No  A's . 

160 
(80)2xl60---1024000,  Ans. 

(24)  (3^)2X3.1416=38.44-,  Ans. 

(25)  50x. 75=137.50;  $37.50— $27.50=$10. 
.754-.25=$l ;  110-^11=10  da.,  Ans. 

(26)  3+5+7=15;  120-1-15=8. 
8X3=24; 

8X5=40; 
8X7=56,  Ans. 
(27^    (30) 2 X. 7854=706.86+;  f  of  706.86+=471.24+. 
^47 1 .24 -r-  .7854=24.49+ ;  30—24.49=5.51+. 
J  of  5.51=2.75+  1st. 

J  of  471.24=235.62;  v/235.62-^. 7854=17.31+. 
J  of  C24.49— 17.31)=3.59+  2d. 
\  of  17.31=8.65+  3d,  Ans. 

(28)  2=G.  C.  D.  of  2,  4  and  6  ;  20-^2=10  hrs.,  Ans. 

(29)  J-J=tV;  tV=$20;  H=$240,  Ans. 

(30)  10X2=20;  20+10=30  in. ;  30+10=40  in.  tail  and  head. 
40X2=80  in.,  Ans. 

(31)  rV—3V=?V;  11-^45=45  days,  Ans. 

(32)  (4000+3)2  :  (4000)2  : :  20  :  19.97+,  Ans. 

(33)  v/484-^16=5j^  sec,  Ans. 

(34)  J  of  12=6;  (6)2x16=576  ft.,  Ans. 

(35)  (2)2x16=64  ft.,  Ans. 

(36)  (20)2  :  (30)2  : :  50  :  112^  bu.,  Ans. 
<33l    500X160^.7854=319.1+  diameter. 

Let  l=:radius  of  small  circle. 

\/(2)  2 -(1)2=1.732+;  I  of  1.732+=1.1546+. 

1.1546+1=2.1546;  319.1+ -5-2.1546=148.1+  rds.,  Ans. 


MISCELLANEOUS.  149        \ 


(38)  \^125=5;  ^216=6;  (5)2  :  (6)2  : :  $10  :  $14.40,  Ans. 

(39)  87.96  :  365.25  : :  45  yrs.  :  186.8  yrs.  Mercury  ; 

30636.82  :  365.25  : :  45  yrs.  :  .53-f  or  a  little  over  \  yr.  old, 
Jupiter.     Ans. 

(40)  A  hits  xV  and  B  f  of  the  time ;  TV4-|=Tf  • 
32H-f|=:24,  Ans. 

(41)  1^X160=300;  300X2=600;  600-^20=30. 
\/i30)2+(20)2=36+  rds.,  Ans. 

(42)  (|)^-(J)^=t¥i;  (I)^=t¥t;  ih  '  A  : :  so  :  62^*^  min.,  Ans. 

(43)  Ivet  l=radius ;  n/(2)  2— (1)2=1.7324-  alt.  of  triangle.. 
]  .732X1=1.732  area  of  triangle. 

(2) 2 X. 7854=3. 14 16  area  of  circle. 
J  of  3.1416=1.5708+  area  of  sectors. 
1.732— 1.5708=.161-f-  inclosed  space. 
.161  :  160  rds. : :  (1)^  :  993.788+. 
>/993.788+=31.5+  radius;  31.5X2=63+  rds.,  Ans. 

(44)  \/(12)  2x4=24,  Ans. 

(45)  5X4=20;  20-^2=10  sq.  ft,  Ans. 

(46)  $2500X(100— 5)=$2375. 

$2500  X  6  %  X  2=$300 ;  $2500+$300=$2800. 

$2800— $2375=1425  int.  for  2  yrs. ;  $425h- 2=$212.50  for  1  yr. 

$212.50-^$2375=8if  %,  Ans. 

(47)  16^^(2x7x2x9)=xV8;  tVtX4=xV8;  tV8X5=xVf; 
*XrV8=/oV6;  43560^7^^=508032,  Ans. 
S2_p2  (108)2— (36)2 

(48)   =base  or  =48  base; 

2S  2X108 

108—48=60  ft.  hypotenuse,  Ans. 

(49)  If4-A=!§;  ioooo-i-ft=640o. 

v/10000— \/6400=20 ;  20-5-2=10  yds.,  Ans. 

(50)  \/(10)2+(10)  2=14.14+  ft.,  Ans. 


I50  MISCELLANEOUS. 


(51)  (4)3=64  cu.  in.;  64+61=125;  ^125=5;  5—4=1; 
l-j-2=^  in.,  Ans. 

(52)  5280  ft. ^840^=6.2832  ft.  cir.  of  wheel. 
6.2832^3.1416=2  ft,  Ans. 

(53)  5  :  (195+5)  : :  5  :  200  radius  hid. 
(200X2) 2 X. 7854=502656  sq.  ft,  Ans. 

(54)  (12+2)  X  3.1416=43.98+,  Ans. 

(55)  3957.5  miles  radius  of  the  earth  at  that  point ; 
3.65+  miles  height  of  Mt  vSt  Blias  ; 
v/3957.5X3.65x2=169.9+  miles,  Ans. 

(56)  \  A=80  sq.  rds. 

80-5-5xl=l«;  \/l6=4  width;  4x5=20  length,  Ans. 

(57)  (168^12)-(98--7J)=if ;  HX7J=$7. 
$7-T-5=$1.40,  Ans. 

^^^^   ^^Igolioll^    1=24;  H=36oz.,  Ans. 

(59)  24  min.=6°;  16°  18^— 6°=10°  18^  W.,  Ans. 

(60)  880-^4=220;  432^4=108. 
220—108=112 ;  (12)  2=144. 
\/l44+112=16  ;  16—12=4  in.,  Ans. 


(61)  \/(40)  2+ (8)2=40.7+  length  of  the  ladder. 
\/(40.7+) 2— (40— 10)  2=27.64+  ft.,  Ans. 

(62)  \/(20) 2x2=28+ ft;  28+^2=14+. 
V (20)  2 + (14+)  2=24.49+  ft,  Ans. 

(63)  40X^=60  in.=5  ft;  5-f4=|;  (|)2=ff. 
43560 -^ff =278781  A,  Ans. 

(64)  (16-^2)2=64;  64X16=1024  ft,  Ans. 


(65)  16X16=256;  i|  of  256=60;  \/256— 60=14 
16—14=2;  2-^2=1  rd.,  Ans. 

(66)  5760  :  7000  : :  160  :  194+,  Ans. 


MISCELLANEOUS.  151 


(67)  \/lOx  160=40 ;  40X16J=660  ft. 
660  X  ^  X  5  X  4=6600  sq.  ft. 
(6600 -r- 1000)  X  $8=152.80,  Ans. 

(68)  96-h8=12;  (12-4-2)  X  12x8=576  sq.  ft,  Ans. 

(69)  6,  8  and  10  are  in  proportion  as  1,  1^  and  If. 
12xli=16;  12xli=20;  12,  16  and  20=sides. 
(12+16-f20)-;-2=24. 


>/24x  12X8X4=96  rds. 
(96^160)  X$850=$510,  Ans. 

(70)  yij-f-i^(r=i  hr.  to  go  1  mi.  and  return. 
4-Hj=24  miles,  Ans. 

(71)  (6)  2-4-(4)  2=2J  times,  Ans. 

(72)  4-j-2=6;  6-T-3=2  each.     A  furnishes  the  pies  for  C  and 

gets  the  10  cts.,  Ans. 

(73)  (1)  ^  X  .7854  X I  of  2=.5236  solidity  of  cone. 
^.5236-7-.5236=l  ft.,  Ans. 

(74)  9Jx3Jx1tVX1728=62244cu.  in. 
62244-7-2150.42=24+ bu.,  Ans. 

(75)  $72.50— 150=$22.50. 

8J%  of  150  for  1  yr.=$4.25. 

22.50 

=5  yrs.  3  mo.  16  da.,  Ans. 

4.25 

(76)  il+A=H;  -H  of  12=17;  17-12=5. 
5— l^=3J  p.  M.,  Ans. 

(77)  (5)2  :  (10)2  ::500:  2000. 
2000  X  (20-j-10)=4000,  AnS. 


(78)    (6)2=36;  (18)2=324;  \/36x  324=108. 
(36-1-1084-324)  xi  of  20=3120  cu.  f . 
3120-^12=260  ft.,  Ans. 


152  MISCELLANEOUS. 

(79)    (5) 2 X. 7854=19.635. 
(10)  2  X. 7854=78.54. 


n/19.635X  78.54=39.27. 

(19.635+39.27+78.54)  X(i  of  20X12)H-144=7.7+  ft,  Ans. 

(So)    (5)3  :  (6)3  : :  120  :  207+  lbs.,  Ans. 

(Si)   9-8^=^;  9-^|=18,  Ans. 


(82)  \/5400-j-6=30  side  of  cube. 
(30)  3=27000  cu.  in.,  Ans. 

(83)  15-^12=1^;  15—10=5;  5-^-1^=4,  Ans. 

(84)  (8VX40)+(^VXl2)=n;  f^-n=lf. 
16-51^=8  da.;  40— 8=32dday,  Ans. 

(85)  60h-12=5;  30x5=150  in.;  150^3.1416=47.7+. 
47.7-7-2=23.8+  in.,  Ans. 

(86)  80X|3=$240;  $240— $150=|90. 
$90-^(3+l)=22J  da. ;  80— 22^=57J  da.,  Ans. 

(87)  (5)2  :  (12^)2  : :  100  :  625,  Ans. 

(88)  (10)  2  X  J  of  20=666f ;  666f -^2=333J. 
^(20)3  :  666f  \\  {x^  \  333^=15.8+. 
20— 15.8+=4.2— ,  Ans. 

(89)  (20)3  .  (10)3  ::  10:1  J,  Ans. 

(90)  60-5-15=4;  2X4=8;  ^-^=8;  if =96  in. 
96^-3.1416=30+  ;  30+^-2=15+  in.,  Ans. 

(91)  6^2=3;  3—^=2^;  6— 2J=3J. 

Z\ 
3J+2J=6;  —of  200=1161. 

6 
2J 

—  of  200=83^  Ans-. 
6 


MISCELLANEOUS. 


153 


(92)  3ft.=36in.;  (36) 2 x. 7854=1016.8784  sq.  in. 

A  I,  B  2V  and  C  i ;  f  of  1016.8784=406.75  sq.  in.  A's ; 
■/o  of  1016.8784=355.907  sq.  in.  B's ; 
\  of  1016.8784=254.219  sq.  in.  C's,  Ans. 
J8^°To  find  what  part  of  diameter  each  grinds  off,  see 
rule  to  find  diameter  of  circle. 

(93)  50 X. 25=112.50 ;  $12.50-7-.40=31^  gal. 
50— 3U=18f  gal.,  Ans. 

(94)  iXj=TV;  1728-^{TVXl2)=2304ft.,ANS. 

(95)  200X160=32000  rds. 

40-1-2=20;  (20)2=400;  \/32000-f-400=180. 
180—20=160  rds.  shorter  sides  ; 
160+40=200  rds.  longer  side,  Ans. 

(96)  20X160=3200;  n/3200=56.5-!-. 
56.5X4X$3=$678,  Ans. 

(97)  N/(32)2-f  (12)  2=34.1+  ft.  slant  height 
24X3.1416=75.3984  cir. 
'75.3984X34.1 

-i-9=142.8+sq.  yds.,  AnS. 


\  2 

(98)  7JX  160=1200;  (50)2=2500;  1200X2=2400. 
\/2500+2400=70  sum  of  sides. 

\/(50)  2— 2400=10  diff.  of  sides. 

(70— 10)-T-2=30  shorter  side ;  30+10=40  longer,  Ans. 

(99)  (10)3 X. 5236=523.6  cu.  in.  solidity. 
523.6-1-3=174.3+ ;  523.6—174.53=349.07. 
\K349.07-;-. 5236=8.7;  10—8.7=1.3+  1st. 
349.07—174.53+  =174.54. 
^174.54-7-.5236=5.5+  in.  3d. 
8.7—5.5=3.2+  in.  2d,  Ans. 


154  MISCELLANEOUS. 

(loo)   40  for  $40=$1.00  each. 
28    "   $35=  1.25    " 

12  .25 

40—35=5=1^2  of  extra  scholar. 
y\  of  .25=.10xV. 
$1.00H-.10x52=$1.10xV 
35X$1.10y\=$38.64372,  Ans. 

(loi)    (13)  2  X  .7854=132.735+. 
(8  J)  2  X. 7854=56.74+. 
\/l32.735  X  56.74=86.78+. 
132.73+56.74+86.78+=276.25+. 
276.25+ X  (J  of  8|)-^231=3  gal.  1  qt.  1—  pt.,  Ans. 

(102)  $60X2=1120;  $120+$60=$180. 
1+4=1 ;  f =$180 ;  1=180  2d  horse. 
$120— $80=$40  cow,  Ans. 

(103)  10X3=30;  30—10=20;  2X2=4;  4—2=2. 
20+2=22  yrs.  son's  age. 

^=22 ;  1=44 ;  44+2=46  father's  age,  Ans. 

(104)  $540— $300=$240 ;  $300— $240=|60. 
1-1+40=60;  i=20;  |=80  days  2d. 

f  of  80=60 ;  60+40=100  days  1st,  Ans. 

(T05)    By  the  reading  of  the  problem  we  can  see  that  the  head 
and  tail  together  weigh  4  lbs. 
4X2=8  lbs.  body;  8+4=12  lbs.,  Ans. 

(106)  ^=16  times+6 ;  1=48  times+18. 
(134+80)— 18=196  ;  196-4- (48+1)  =4  ft. 
134—4=130  ft.,  Ans. 

(107)  5X2=10;  (10) 2 X. 7854=78.54 

78.54X  {\  of  6)  X  1728-7-4=67858.56  cu.  in. 
67858.56-5-2150.4=31.55+  bu. 
31.55+X$1=431.55+,  Ans. 


MISCELLANEOUS.  155 

(108)  Am't  of  $1  at    6%  for  6  yrs.=$1.36 

"      "       "      10%    •'   3    "   =11.30 

.06 
$300h-.03=$5000,  Ans. 

(109)  1859     5     12  Int.  on  $1  for  1  yr.  8  mo.  24  da.  is  .10?  ; 
1857     8     18  $26-^.1  Of =$250,  Ans. 


1     8    21 

(no)    507-^3=169;  \/Wt 

1=13,  Ans. 

0       /      // 

(III)        31    27    30 
2    30 

hr.  min. 
14      2 

2      6 

15)31    30 

11     56  Ans. 

2  hr.6  min. 

(112)  $1+.20=$1.20;  120  cts.X  4=480,  Ans. 

(113)  6%  of  $660  for  1  yr.=$39.60. 
$213.40-r-$39.60=5xV  yr.=5  yr.  4  mo.  20  da.,  AnS. 

(114)  The  minute-hand  moves  60  min.  while  the  b'^ur-hand 

moves  5  minutes  and  gains  55  minutes. 
60-T-55=ljV  min.  to  gain  1  min. 
25—14=11  min.  to  be  gained. 
l^ij-X  11=12  min.  past  5,  Ans. 


(115)  (8)3=512;  v/512X.22|=10f,  Ans. 

(116)  Int.  on  $1  for  23  da.=. 003625. 
$7.25-T-.003625=$2000,  Ans. 

(117)  Wife  receives  3  times  as  much  as  daughter,  son  3  times 

as  much  as  wife. 
fX 3=1  son;  f =wife  ;  i=daughter. 
9-1-14- J==-\3;  1^3=16591;  1=1507  daughter. 
f=$1521  wife ;  |=$4563  son,  Ans. 


T56  MISCELLANEOUS. 

(ii8)   48—27=21;  484-21=69;  90—69=21. 
90+(2lX3)=153 ;  174—153=21,  Ans. 

(119)*  9+15=24;  M-2'i==iV 

■i^  of  $24=16 ;  if  of  $24=$15 ;  64-15=$21  B. 
$24— $21=«:$3  A,  Ans. 

(I20)   $.11— $.10^=^ct.;  30+15=45;  45-r-J=90  lbs.,  AnS. 

(i2i)   5  pears  +  6  peaclies=:28  cts. 
6      "     +3        "      =21    " 
And  12  pears  +  6  peaches=42  cts. 
5      «     +6       "       =28    " 


7  pears= 

14  cts. 

1      "    = 

2    « 

1  peach= 

3   «  Ans. 

(122)   10  at  50^=$5.00. 

$5-=-4=$1.25  each  pays. 

$1.25X  (10— 2+4)=$15,  Ans. 

(123)  40  :  ;^ : :  40  :  10=40,  Ans. 

40:10 

(124)  3+4+5=12;  136-4-12=11^. 
11^X3=34  yr.  A;  11JX4=45J  yr.  B. 
llJX5=56f  yr.  CANS. 

(125)  |=$4500;  |=$7500. 
$7500—14500=13000,  Ans. 

(126)  t\=1188;  ^1=4556;  n/4556=66,  Ans. 

(127)  20  pupils  for  $20=$1.00  each 
12      "        "    $15=$1.25    " 

8  .25 

20—17=3. 
I  of  .25=.09|. 
($1.00+.09f)Xl7=$18.59f,  Ans. 

(128)  v/9x4=6,  Ans. 


MISCELLANEOUS.  157 

(129)   250 X. 02=5;  9-J-5=lfyrs. 

A's  is  to  B's  as  1  to  3  or  I  and  f. 

\oi\=\\  t  of  3=2. 

2%  of  i  for  If  yrs.=.018  ; 

2%  of  2  for  If  yrs.=.072  ; 

.018-f  .072=.09  sum  of  interests. 

.09X25X10=22.50. 

($180-5-22.50)  X  100=$800. 

I  of  $800=1200  A's  ; 

I  of  $800=$600  B's,  Ans. 


(130)  >/(15)  2 --(7^)2=12.94-;  i  of  12.9-h=4.3-}-. 
4.3-fX  2=8.6+,  Ans. 

(131)  \/(3)2  4-(4)2=5  in.,  Ans. 

(132)  v/ (60) 2x^7854=53.1+  rds.,  Ans. 

(J33)   \  A=21780  sq.  ft. ;  21780-^3=7260  ft,  Ans. 

(134)  173.2X2=346.4. 
\/340=18.61+,  Ans. 

(135)  2+3=5;  125-i-5=25;  \/25=5. 
5X2=10. 

5X3=15,  Ans. 

(136)  3+4=7 ;  f  of  Z\—\\  ft.  from  strong  man,  Ans. 

(137)  12X5^=.60;  .60— .20=40^. 
(40xl00)-r-20=200%,  Ans.    . 

(138)  100-^1^  of  .005=2000000,  Ans. 

(139)  1+1=1;  $3-H=$lf  B;  $3-$lf=$lf  A.  Ans. 

(140)  (18)  2+(6)  2=360;  360-r-2=180. 
v/l80=13.4;  13.4—6=7.4. 
18X12=216;  18—6=12;  216-^-12=18. 
\/l8x  7.4=11.5+;  18— 11.5+=6.5  ft.,  AnS. 

(141)  12X12=144;  (12+2)-r-2=7  ;  144x7=1008. 
(144x2)^-2=144;  10—2=5;  J  of  144X5=240, 
(1008+144+240)-r-144=9f  ft.,  An^, 


i.,S  MISCELLANEOUS. 


(142)   v/7075t)-T-4=133  width  ;  1^3x4=532  length. 
(133+532)  X  2=1330;  l330-r-7=190,  Ans. 


(143)  \/9x  16=12,  Ans. 

(144)  (12xl6)-7-(12+16)=6.84-,  Ans. 


(145)  (30)2=900;  N/f  of  900=24.54- ,  Ans. 

(146)  625-7-62.5=10  cu.  ft.,  Ans. 

(147)  8-T-(8— 6)=4,  Ans. 

(148)  $1  at5%  for8yrs.=.40;  , 
$800-T-.40=$2000,  Ans. 

(149)  25+20+15=60;  60-7-2=30  half  sum. 

\/30X5XlOX  15=150  area  of  triangle. 

(150X2) -7-25=12  ft. ;  12+i8=30  ft.  height  of  house,  Ans'. 

(150)  $375-7-175=5  A.  ^      .  .;    . 
5X160=800  sq.  rds. 

\/800X2=40  rds.     1  side. 
40X3=120  rds.,  Ans. 

(151)  The  hour-hand  moves  a  certain  distance  from  5.    The 

minute-hand  must  gain  25  minutes+2  dis.  from  5, 
While  the  hour-hand  moves  1  dis.  the  minute-hand 
moves  12  dis. 

.*.  25  min.+2  dis.=12  dis.  or  25  min.=10  dis. 

25-7-10=2J  min.  hour-hand  moves. 

2Jxl2=:30  min.  minute-hand  moves,  Ans. 

(152)  3+2=5;  f  of  10=6;  f  of  10=4. 

(6-1-2)  X  (4-r-2)=6  ;  '43560  ft.-7-6=7260,  Ans. 

(153)  3  X  15°=45°  east,  Ans. 

(154)  \/(80)2+(100)  2=128+  ;  \/(100)2+(100)  2=141+. 
128+Hl+«269+ ft.,  ANS. 


MISCELLANEOUS.  159 

(155)  The  money  will  run  10  and  5  yrs.  respectively. 
Am't  of  11  at  10%  for  10  yrs.=$2.00 

"        "         "       «         5    "  =$1.50 

$3.50 
$1400-v^3.50=$400 ;  $400Xl.50=$600. 
$400X2.00=$800,  Ans. 

(156)  168-4- 2=sum  of  2  sides=«S=84. 
If  X=one  side,  S — X=other. 

X(S -X)=area=10|X  160=1728  sq.  rds. 
\/X2— 84  X4-(42)  2=v/l764— 1728. 
X— 42=i  6.     Sides=42+6=48  and  42— 6=36,  Ans. 
Note.— Many  of  the  solutions  of  problems  in  this  list 
can  be  explained  by  such  general  formulae. 


<157)   \/(2)  2— (1)2=1.732;  1.732X3=5.196  area  of  triangle, 
(4) 2 X. 7854=12.566  area  of  wheel. 
(12.566—5.196)^-3=2.456  part  in  the  water. 
2.456 

=.195+,  Ans. 

12.566 

(158)  (100)2  :  (200)2  : :  4  :  16  da.,  Ans. 

(159)  6—4=2 ;  1=12  ft. ;  |=36  radius. 
36X2=72  ft.  diameter,  Ans. 

(160)  128-r-3.141 6=40.74+  diameter. 
40.74^2.15474-=18+,  Ans. 

(161)  \  of  (754-90)=82|  rds. ;  \  mi.=160  rds. 
(160X82^)4-160=82^  A;  82J^X$80=$6600,  Ans. 

(f62)    (10) 2 x.7854x^  of  15=392.7  solidity  of  cone ; 

(5)  2  X  .7854 X  30^ X  9=5345.622+  area  of  land ;  ) 

392.7 H-5345.622+=.0734+  ft.,  Ans. 

(163)    (6)  2  X  2.828+  =101.80+  cu.  in.,  AJSrs. 


i6o 


MISCELLANEOUS. 


(164)    1st  term  .03 ;  No.  terms  11 ;  ratio  8. 
(8)iox$.03=$32212254.72  last  term. 
$32212254.72X8 
: =$36814005.39,  Ans. 


\-\) 


14  /{10)2        (14)2        (14)2 

=-+J +-    =7+1=8. 

-      ^    -  2  4 


(165)   Sid 

2       '    2 
14—8=6,  Ans. 


(166)  P.  W- of  $6400  for  8  mos.  at  6%=$6186.67-f  . 
$6400— $6186.67+=$213.33—  dis. 

$213.33— (5%  of  $6186.67  for  8  mos.)=$7.11-j-,  AnS. 

(167)  f=f;  l=A;  T%+i^=H;  i§=.625D;  ^^=.375  a. 
.375-f^Am't  of  $1  for  6  yrs.=.23xV 


.625- 


((      «     «     « 


($290-^.7511)  X.23x^^=$90 
($290  ^  .75|f )  X  .52f^=$200,  Ans. 

(i68)   20=G.  C.  D.  or  side  of  each  field. 
(320^20)  X  (180h-20)=144,  Ans. 

(169)    (20)  2  X  16=6400  ft.,  Ans. 

(170) 


CD=1 


OC=\/P +12=1.414. 
OP=1.414+l=2.414. 
OP:(CP=CD)  ::10ft.:(X). 
2.414  : 1  : :  10  ft. :  4.14,  Ans. 


MISCELLANEOUS.  i6i 


225 

(171)  (7i)2=— . 

4 
225 

904^i  ft.-T- =16tV  ft.,  Ans. 

4 

(172)  \/(12)2— (35X4)=2,  Ans. 

(173)  (16^2)+(2h-2)=9. 
(16-^2)— (2-^2)=7,  Ans. 


(174)  (3)2=9;  J^  of  9=2.25;  n/1  80+2.25=13.5. 
13.5— (i  of  8)=12. 

12+3=15,  Ans.  . 

(175)  [(7)3-133]-4-(3x7)=10. 
\/{7)2-10x4=3 ;  (J  of  3)+(J  of  7)=5. 

7—5=2,  Ans. 

(176)  4x(v/2+l)=9.656+;  9.656+X2=19.31+,  Ans. 


(177)  v^i  of  (41— 9)=4. 
\/41— 16=5,  Ans. 

(178)  (19)2—193=168. 

\/l93— 168=5 ;  J  of  (19—5)=  7. 

19—7=12,  Ans. 

(179)  65-(7)2=16. 
\/65+16=9. 

(i  of  9)+(i  of  7)=8. 

9—8=1,  Ans. 

(180)  20-^12=1  J. 
1X3.1416=3.1416. 


%/(!§)  2+(3.1416)  2  X  12=42.79+  ft,  Ans. 

(181)   $12X7=$84;  $5xl2=$60;  84— 60=$24. 
12-t7=5;  $24h-5=$4.80,  Ans. 


i6*.  MISCELLANEOUS, 


(182)    (6)3  :  (3)3  : :  25  :  3.12+  lbs.,  Ans. 


(183)  (3)2+ (5)2=34;  %/30600-^34=30. 
30X3=  90. 

30X5=150,  Ans. 

(184)  |=$1200;  |=$2000;  |1200+$500=$1700. 
$2000— $1700=1300,  Ans. 

(185)  4x3=12,  difference  between  the  youngest  and  oldest. 

1=12;  1=24. 
24  —  4  =  20. 
20  —  4  =  16. 
16  —  4  =  12,  Ans. 

(186)  A  has  3  times  as  many  as  B. 
J+f=f;  60h-|=45A. 

\  of  45=15  B,  Ans. 

(187)  8=G.  C.  D.;  (8)2=64,  Ans. 

(188)  $5^(Hf— ifif)=$89.90,ANS. 

(189)  4500  :  3000  : :  27  :  11 

1800  :  (1100).  Ans,  1100  mi. 

(190)  (8 -J- .866)  X  3.1416=28.99+,  Ans. 


(191)  %/[  (100)2 +2800]-^2=80. 
\/(100)  2— 2800=60. 

(80  X  60) -H  160=30  A,  Ans. 

(192)  135-^9=15;  15+9=24. 
24-^2=12. 
12—9=3,  Ans. 

(193)  (10)  2  X  .7854=78.54  area  of  circle. 
>/(10)  2— (5)2=8.66+. 

8.66  X  5=43.3  area  of  triangle. 
43.3—1  of  78.54=4.03  sq.  ft.,  Ans. 

(194)  60xl.l54x3x.80=$166.17+,  Ans. 


MISCELLANEOUS.  163 


(195)   24X2.41+ =57.84+  side  of  field. 
(57.84)2-^160=20.9+  A,  Ans. 


(196)   J24-4-2)2=144;  \/l44— 140=2  diflference  of  sides. 
\/l44=12;  12+2=14. 

24—14=10,  Ans. 


(197)  4-^2=2;  \/l40  +  (2)2=12. 
12+2=14. 

14— 4=10,  Ans. 

(198)  [(30)2— (6)2]-^2=432. 

>/432  +  (3)2=21;  21+3=24;  24—6=18. 
18X24=432,  Ans. 

(199)  >/2&=5;  5X4=20. 
(20-4-\/25)  2=16,  Ans. 


(200)  \/420— 224=14  C. 
224-^14=16  J,  Ans. 

(201)  1  :  ^  : :  10  :  2J  ft.,  Ans. 

(202)  6  of  the  smaller  circles  will  be  tangent  to  the  7th  lo- 

cated at  center,  and  will  touch  the  outer  large  circle. 
15-^3=5  ft.,  Ans. 

(203)  8:10::l:(l^ft.},  ANS. 


(204)  n\\h\\ :  (18)  2 :  v^37:6=15.4. 
18—15.4=2.6  ft.  1st  piece. 

1\  :  3J  : :  (18)  2 :  ^l5i:2=12.3+. 
18—12.3=5.7  ft.  2d  piece,  Ans. 

(205)  lOX  (2— >/3J=2.68+  in.,  Ans. 

(206)  12X|of  (6+4)=60. 
12x5Xi=  20 

80  ft,  Ans. 


i64  MISCELLANEOUS, 

{207)    (74-17)  X  30=720;  720-7-2=360. 

17—7=10;  17x6=102;  ^  of  102x17=867. 
867—360=507 ;  \/507x 2x6=78  rds. 
102  rds.— 78  rds.=24  rds.,  Ans. 

(208)  3  : 1  : :  10  :  3J,  Ans. 

(209)  12-7-1.154=6.9-1- ft. 

or  (x/242— 122)-^3=6.9-}-ft.,  Ans. 

(210)  1.0-^=$1.01;  lOX $1.01=110.10,  Ans. 

(211)  300-i-6=50  lbs.,  Ans. 


(212)  >/\  of  (74)2=52.34-  ft.,  Ans. 

(213)  L.  C.  M.=2520 ;  25204-5=2525,  Ans. 


(214)  (3)24.(4)2=25;  n/ (60) ^--25=12. 
12X3=36. 

12X4=48,  Ans. 

(215)  104-r-2=52;  3X160=480. 
(52^2)2=676;  v/676— 480=14. 
26  4-14=40. 

480^40=12,  Ans. 

(216)  (2)  2 :  (4)  2 : :  300  :  1200  ft.,  Ans. 

(217)  (10) 2 X. 7854X^=39.27  cu.  ft..  Ans. 

(218)  (3) 2 X. 7854=7.0686. 
(56x3)-^7.0686=23.764-  ft.,  Ans. 

(219)  \  of  (204-15)=17.5;  (17.5) ^X. 5236=28064-  cu.  ft.,  Ans. 

(220)  12-T-3=4  ;  4=side  of  equilateral  triaugle. 
6.164"  =area  of  equilateral  triangle. 
6.16  :  43560  ::  1  :  70714-  A,  Ans. 

(221)  100X80X120=960000. 

Area  of  triangle  whose  sides  are  100,  80  and  120=39684-. 
Q60000~-(3968x4)=60.484-,  Ans. 


y^ri^CELLANEOUS.  165 


(222)  v/(12) 2— (6)2=10.3;  (10.3xl2)-^(10.34-12)=5.oin.,  Ans. 

(223)  (6x8)-=-{6+8)=33„Ans. 

(224)  In  the  triangle  ABC,  let  AB=12 ;  BC=16  ;  AC=20. 
Bisect  the  angles.    The  point  of  intersection  O  will  be 

the  center  of  the  circle.  From  O  draw  OM  perpen- 
dicular to  AB ;  ON  to  BC ;  OP  to  AC.  In  the  3  pairs  of 
equal  triangles  AP=AM ;  PC=CN;  BN=BM.  Perim- 
eter=2  APH-2  PC-f2  BN=48. 

(H-2),  AP+PC+(BN=OM=R)=24. 

AP-|-PC=20. 

24— 20=4  R;  4x2=8  diameter,  Ans. 


(225)  v/(20.5) 2— (4.5)2=20;  20x4^X2=180. 
20+204-9=49;  180-^9=3.6+. 
3.6+  X  2=7.2+  ft.,  Ans. 

(226)  5-5-5|f%=92%,  Ans. 


(227)  V\  of  (20)2=14.1+. 
(14.1)2x1=80  sq.  in.,  Ans. 

(228)  (5)2+(7)2=74;  518^74=7. 
(5)2x7=175. 
(7)2x7=343,  Ans. 

(229)  3.1416  :  5  : :  10  :  Ans.=15.9+  miles,  Ans. 


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one  who  is  engaged  in  teaching  or  is  intending  to 
teach,  particularly  Normal  Students.  We  desire  to 
introduce  it  into  every  Teachers*  Reading  Circle. 
After  reading  the  book  you  will  want  to  help  us. 
May  we  send  you  a   sample  copy  on  approval  ? 


\ 


HiNDS  &  NOBLE,  Publishers 

31-33-35  West  15th  St.  New  York  City 


Best  Methods  of  Teachin 
in  Country  Schools 

By  G*  Dallas  hind 


This  work  is  not  the  fine-spun  theory  of  a  college  pro- 
fessor, but  the  practical  ideas  of  a  country  teacher,  fresh 
from  the  country  school-room. 

It  is  not  a  mass  of  "  glittering  generalities,"  but  sug- 
gestions in  detail  as  to  how  to  teach  and  manage  an  un- 
graded school,  drawn  from  long  experience  and  careful 
observations. 

1.  //  /^//j  Aow  the  teacher  should  conduct  himsdf  in  rela- 
tion to  his  patrons  and  to  society  in  general, 

2.  It  tells  what  qualifications  are  necessary  for  a  good 
teacher. 

3.  //  tells  how  to  apply  for  a  school. 

4.  It  describes  in  detail  the  most  approved  and  appli- 
cable methods  of  teaching  all  the  branches  studied  in  a 
country  school. 

5.  It  gives  some  very  practical  hints  about  apparatus  and 
school  architecture. 

6.  It  will  give  you  new  insight  into  your  work. 

7.  It  will  lead  you  to  see  and  realize  more  pleasure  and 
happiness  in  your  teaching  than  you  have  ever  been  able  to  get 
cut  of  it  before. 

8.  It  will  give  you  the  essential  principles  of  practical 
teaching. 

9.  //  will  tell  you  Just  what  to  do  and  how  to  do  it,  so  that 
four  work  will  not  only  be  enjoyable^  but  profitable. 

No  book  has  ever  been  published  containing  so  many 
helpful  suggestions  of  vital  interest  to  Teachers  of 
Country  Schools. 

Teachers  of  Town  and  City  Schools  will  also  derive 
much  benefit  from  reading  the  Chapters  on  the  Methods 
of  Teacljing.  Reading,  Spelling,  Arithmetic  Geography, 
General  Historv.  Physiology.  Algebra.  Natural  Science, 
Morals  and  Manners. 


A  sample  copy  will  be  sent,  postpaid,  to  any  teacher  for 
$1.00  (regular  price  $1.25). 

HINDS  &  NOBLE,  Publishefi 
3J  33-35  West  I5th  Stre^*.        -         New  York  Qty 


For  Teachers  And  Students 


Ce$$on$  Outlined 

tn 

U.  S.  History^  Geography^  English  Grammar 

Physiology  and  Arithmetic 

By  G*  Dallas  Lind 

Author  of  "Best  Methods  of  Teaching  in  Country 
Schools " 

Cloth,  224  pages,    200  Lessons.     Regular  price,  $1.2^ 
(  To  Teachers,  $1.00^ 


A  Specimen  Outline  Lesson  in  U.  S.  History- 
Outline  Lesson  LVH  5 
McKinley's  Administration 

''^  The  peace  we  have  won  is  not  a  selfish  truce  of  artnt^ 
but  one  -whose  conditions  presage  good  to  hutnanity. 

Explosion  of  the  "  Maine  " 

Spanish- American  War  : — 

Dewey  at  Manila 

Sampson  Bombards  San  Juan 

Sinking  of  the  "  Merrimac" 

Schley  Destroys  Cervera's  Fleet 

Stamp  Tax 

Battles  of  El  Caney  and  San  Juan  HHl 

Ponce  Surrenders  to  General  Miles 

Manila  Captured 

Annexation  of  Hawaii 

Treaty  of  Peace  Signed  at  Paris 

Peace  Conference  at  the  Hague 

War  with  the  Philippine  Insurgents 

See  Montgomery's^  McMaster''s^  Lee's  or  any  other  recent 
History  0/  the  United  States. 

Have  your  pupils  write  a  brief  account  of  the 
Spanish-American  War. 

HINDS  &  NOBLE,    ^    ^    jfL    New  York  Qty 


Teacbers,  Piipns,  Candidates* 
ATTENTION ! 

The  most  experienced  teachers  hare,  after  caitfol 
preparatior ,  published  three  wonderful  books. 

In  the  first  one  they  have  put  all  of  the  Common 
branches,  over  a  dozen  in  all,  and  then  have  written  each 
branch  in  questions  and  then  answered  each  question  in 
full,  making  over  Seven  Thousand  Questions  with  the 
Seven  Thousand  Answers,  completely  exhausting  Gram- 
mar, Geography, Arithmetic,  History,  Physiology,  Spelling, 
Reading,  etc.,  so  that  any  one,  right  at  home,  can  become 
greatly  proficient  in  all  these  branches  without  the  aid 
of  a  teacher.  This  first  book  is  worth  fifty  dollars  o{ 
anyone's  money  in  preparing  a  teacher  or  student  or 
civil-service  candidate,  for  examination,  and  the  book 
sells  for  only  $1.50. 

The  second  book  takes  up  twelve  Normal  branches 
in  the  same  way,  thus  being  very  desirable  for  students 
who  are  fitting  themselves  to  teach,  also  for  teachers 
who  are  studying  for  examinations  for  higher  grade  certifi- 
cate. 

And  the  third  book  takes  up  the  High  School 
branches  and  exhausts  them  in  a  like  manner,  so  any  one 
wishing  to  prepare  for  college  can  use  this  one. 

For  special  description  of  each  of  these  three  books 
separately  see  the  following  pages  of  this  leaflet. 

If  you  return  this  leaflet 

with  your  remittance  you  may  deduct  jo  cents  if  you 
order  one  of  the  books;  deduct  yj  cents  if  you  order  any 
two  of  them;  deduct  $1.25  if  you  order  all  three  of  tl>e 
^ooks. 


Wby  Did  He  Do  It? 

The  froblishei*  of  a  well-known  "lescchers*  monthly  h«vio| 
too,ooo  circulation,  knowing  by  experience  thai 
no  premium  for  subscribers  is  so  attractive  to  teachers 
as  a  good  question  book,  selected  for  that  purpose 
craig's  common  school  question  book.  He  has  dis- 
posed of  over  twenty  thousand  copies  of  it  up  to  now. 
The  manager  of  said  iubnthly  is  a  level-headed  publisher  and 
a  clever  business  man;  and  he  knows  just  how  to  supply 
the  high  quality  of  merit  demanded  by  teachers  in  whs^ 
they  read  and  study,  else  he  could  not  have  built  up  tho 
wonderful  success  which  his  monthly  admittedly  is,  with 
its  unprecedented  list  of  over  100,000  subscribers!  He 
tells  why  he  selected  Craig's  Question  Book,  in  a  full  page 
announcement  in  his  paper,  addressed  to  the  teachers  of 
the  United  States.  The  following  zvords  are  wholly 
kiSt  and  his  alone;  not  an  inkling  of  them  had 
reached  us  previous  to  his  printed  announcement: 

stands  the  Test 

TberO'are  Question  Books  and  Question  Books,  good* 
bad  and  indififerent,  all  of  more  or  less  value,  but  there  is 
only  one  that  can  really  be  classed  as  standard  and  this 
one  is  so  pre-eminently  superior  to  all  others  that  it  Is 
Instinctively  classed  asttie  leader.  Craig's  Question 
Book  has  this  distinction  and  justly, so.  There  is  no  more 
critical  class  of  buyers  in  the  world  than  the  American 
school  teachers  and  when  any  single  book  devoted  to  their 
Interest  is  purchased  by  192,000  of  them  (this  is  the  record 
of  Craig's  up  to  Dec.  31,  1902)  it  must  have  an  abundance 
of  real  merit  back  of  it.  Such  has  been  the  record  of 
the  past  and  its  future  promises  to  be  even  more  success* 
ful  than  its  past  has  been. 

Thoroughly  Revised, 

Enlarged  and  in  every  way  improved — made  Over  in  fact 
The  publishers  of  this  great  book,  ever  on  the  alert  to 
keep  in  the  front  rank,  realized  that  '  y  the  expenditure 
of  a  few  thousand  dollars  it  could  be  m  .de  even  more  use- 
ful in  the  great  field  it  occupies.  They  set  about  the  task, 
and  have  so  thoroughly  performed  the  work  and  improved- 
the  book  to  such  a  degree  that  even  its  old  friends  woul^ 
**k  recognize  it  but  for  the  name. 


How  it  was  done. 

The  entire  book  was  re- written,  reset  in  new  type,  an  elegant 
mew  cover  design  substituted  for  the  old ;  and  printed  on  fine 
paper  substantially  bound  in  doth,  it  presents  an  appearance  as 
attractive  as  the  contents  are  reliable.  In  the  old  edition  the 
Questions  are  tn  one  chapter  by  themselves,  followed  in  the  next 
by  the  Answers,  numbered  to  correspond.  Now  the  Questions 
and  Answers  are  printed  alternately,  the  former  in  Italic  and 
the  latter  in  Roman  type,  thus  adding  to  the  value  of  the  book 
in  exactly  the  same  proportion  as  it  is  rendered  more  handy. 
No  expense  has  been  spared,  nothing  left  undone,  to  bring  this 
work  fully  up  to  date  in  every  sense,  and  the  new  Craig  will 
meet  with  even  greater  favor  than  the  old. 

Our  Motive 

In  selecting  this  book  from  the  dozen  or  more  similar  ones  was, 
perhaps,  a  selfish  one,  because  it  is  so  immensely  popular  (and 
justly  so)  among  the  teachers  of  this  country  that  it  sells  more 
readily  than  any  other.  There  are  others  which  would  yield  us 
a  greater  profit,  but  we  have  declined  to  handle  them  simply 
because  they  lack  the  real  merit  which  distinguishes  this 
work.  We  could  not  afford  to  sacrifice  our  reputation  of  always 
giving  at  tlie  smallest  cost,  the  best  procurable. 

As  a  Real  Help 

In  preparing  for  examinations,  reviews,  etc. ,  a  good  Question 
Book  can  not  be  over-valued,  and  the  teacher  who  possesses 
this  book  can  feel  sure  that  she  has  the  best,  and  always  at 
hand  ready  made  material  for  conducting  those  reviews  so  neces- 
sary to  success.  To  the  average  teacher  any  one  of  half  a 
dozen  departments  in  this  book  is  well  worth  the  price. 

Contents  of  Book. 

An  aggregate  of  nearly  8,000  Questions  and  Answers,  cover- 
ing the  following  subjects,  all  carefully  rewritten  and  brought 
up  to  date :  U.  S.  History,  Geography,  Reading,  Gram- 
mar, Letter  Writing,  Orthoepy.  Orthography,  Pho- 
nology, Written  Arithmetic,  Theory  and  Practice 
Teaching,  Book-Keeping,  Drawing,  Alcohol  and  To- 
bacco, Physiology,  Participles,  Infinitives,  Writing, 
Test  Problems,   Civil  Gov't,  Parliamentary  Rules. 

HINDS  &  NOBLE,  Publishers  of 

Craig's  Common  School  Question  Book,  With  Answers,  $1.50 

Henry's  New  High  School  Question  Book,  With  Answers,  $i.s» 

SherriU's  New  Normal  Questions,  with  answers,  $1.50 

Quizzism,  and  its  Key,  |i.oo 


Some  ne<p  SpeaRm 


The  Best  American  Orations  of  To-day  (Blackstone)    $1.25 

Selected  Readings  from  the  Most  Popular  Novels    •  I.OO 

Pieces  That  lijve  Taken  Prizes  in  Speaking  Contests  1.25 
New  Pieces  That  Will  Take  Prizes  in  Speaking  Contests  1.25 

Pieces  for  E'Ufry  Occasion  (Le  Row)        -        -        -  1.25 

How  to  Attract  and  Hold  an  Audience  (Esenwein)  I.OO 

How  to  Use  the  Voice  in  Reading  and  Speaking  (Ott)  1.25 

Uow  to  Gesture,  New  Illustrated  Ediiion  (Ott)    -  I.OO 

A  Ten  Weeks'  Course  in  Elocution  (Coombs)         •  1.25 

Fenno's  New  Science  and  Art  of  Elocution       -        -  1.25 

Three-Minute  Declamations  for  College  Men  -  1.00 

Three-Minute  Readings  for  College  Girls  •       -  1.00* 

Handy  Pieces  to  Speak  (o«c<7r<fi)     -        •        •        •  .50 

Acme  Declamation  Book  -       -       .       »        .  .50 

Ross'  Southern  Speaker  -       -        -       •       •  I.OO 

New  Dialogues  and  Plays  {Primary,  Inter.,  Adv.)  1.50 

Commencement  Parts  (Orations^  Essays,  etc.)  -  L50 

Pros  and  Cons  {Questions  of  To-day  Fully  DiscusseJ\  1.50 

253  New  Questions  for  Debate         -        -       -       .  .15 

How  to  Organize  and  Conduct  a  Meeting        »        -  ,75 

Palmer's  New  Parliamentary  Manual        -        «        -  .75 

Howe's  Hand  Book  of  Parliamentary  Usage    -        -  J(l 

HINDS,  NOBLE  &  ELDREDGE 
3t-33-35  West  J  5th  Street.  New  York  Cf|C^ 


•  ^ ..', 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 
BERKELEY 

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